Theorem feq23i

Description: Equality inference for functions. (Contributed by Paul Chapman, 22-Jun-2011)

	Ref	Expression
Hypotheses	feq23i.1	$$⊢A=C$$
	feq23i.2	$$⊢B=D$$
Assertion	feq23i	$$⊢F:A⟶B\leftrightarrow F:C⟶D$$

Proof

Step	Hyp	Ref	Expression
1		feq23i.1	$$⊢A=C$$
2		feq23i.2	$$⊢B=D$$
3		feq23	$$⊢\left(A=C\wedge B=D\right)\to \left(F:A⟶B\leftrightarrow F:C⟶D\right)$$
4	1 2 3	mp2an	$$⊢F:A⟶B\leftrightarrow F:C⟶D$$