3 Added a small explanation
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When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class without it's own spell list.

The reason is simple: Classes without a spell list are actually raising another class' spellcasting. These classes always clearly specify that they raise another class' spellcasting.

When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class without it's own spell list.

When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class without it's own spell list.

The reason is simple: Classes without a spell list are actually raising another class' spellcasting. These classes always clearly specify that they raise another class' spellcasting.

2 added 3 characters in body
source | link

When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class withwithout it's own spell list.

When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class with it's own spell list.

When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class without it's own spell list.

1
source | link

When you gain a level in a prestige class that raises your caster level and your spell level from another spellcasting class, the other spellcasting class MUST have it's own spell list.

i.e. You may gain a level in Arcane Trickster to raise the spellcasting levels of Wizard or Assasin because both have their own spell list, but not to raise the spellcasting levels of Mystic Theurge, Archmage, or any class with it's own spell list.