Theorem feq2dd

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

	Ref	Expression
Hypotheses	feq2dd.eq	|- ( ph -> A = B )
	feq2dd.f	|- ( ph -> F : A --> C )
Assertion	feq2dd	|- ( ph -> F : B --> C )

Proof

Step	Hyp	Ref	Expression
1		feq2dd.eq	|- ( ph -> A = B )
2		feq2dd.f	|- ( ph -> F : A --> C )
3	1	feq2d	|- ( ph -> ( F : A --> C <-> F : B --> C ) )
4	2 3	mpbid	|- ( ph -> F : B --> C )