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Metamath Proof Explorer

Theorem feq2dd

Description: Equality deduction for functions. (Contributed by Thierry Arnoux, 27-May-2025)

Ref Expression
Hypotheses feq2dd.eq ⊢ φ → A = B
feq2dd.f ⊢ φ → F : A ⟶ C
Assertion feq2dd ⊢ φ → F : B ⟶ C

Proof

Step Hyp Ref Expression
1 feq2dd.eq ⊢ φ → A = B
2 feq2dd.f ⊢ φ → F : A ⟶ C
3 1 feq2d ⊢ φ → F : A ⟶ C ↔ F : B ⟶ C
4 2 3 mpbid ⊢ φ → F : B ⟶ C