Metamath Proof Explorer

Theorem feq2i

Description: Equality inference for functions. (Contributed by NM, 5-Sep-2011)

Ref Expression
Hypothesis feq2i.1 ⊢ A = B
Assertion feq2i ⊢ F : A ⟶ C ↔ F : B ⟶ C

Proof

Step Hyp Ref Expression
1 feq2i.1 ⊢ A = B
2 feq2 ⊢ A = B → F : A ⟶ C ↔ F : B ⟶ C
3 1 2 ax-mp ⊢ F : A ⟶ C ↔ F : B ⟶ C