Theorem feq3dd

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

	Ref	Expression
Hypotheses	feq3dd.eq	|- ( ph -> B = C )
	feq3dd.f	|- ( ph -> F : A --> B )
Assertion	feq3dd	|- ( ph -> F : A --> C )

Proof

Step	Hyp	Ref	Expression
1		feq3dd.eq	|- ( ph -> B = C )
2		feq3dd.f	|- ( ph -> F : A --> B )
3	1	feq3d	|- ( ph -> ( F : A --> B <-> F : A --> C ) )
4	2 3	mpbid	|- ( ph -> F : A --> C )