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 )