Metamath Proof Explorer

Theorem feq12i

Description: Equality inference for functions. (Contributed by AV, 7-Feb-2021)

Ref Expression
Hypotheses feq12i.1 ⊢ F = G
feq12i.2 ⊢ A = B
Assertion feq12i ⊢ F : A ⟶ C ↔ G : B ⟶ C

Proof

Step Hyp Ref Expression
1 feq12i.1 ⊢ F = G
2 feq12i.2 ⊢ A = B
3 eqid ⊢ C = C
4 feq123 ⊢ F = G ∧ A = B ∧ C = C → F : A ⟶ C ↔ G : B ⟶ C
5 1 2 3 4 mp3an ⊢ F : A ⟶ C ↔ G : B ⟶ C