Theorem feq23d

Description: Equality deduction for functions. (Contributed by NM, 8-Jun-2013)

	Ref	Expression
Hypotheses	feq23d.1	|- ( ph -> A = C )
	feq23d.2	|- ( ph -> B = D )
Assertion	feq23d	|- ( ph -> ( F : A --> B <-> F : C --> D ) )

Proof

Step	Hyp	Ref	Expression
1		feq23d.1	|- ( ph -> A = C )
2		feq23d.2	|- ( ph -> B = D )
3		eqidd	|- ( ph -> F = F )
4	3 1 2	feq123d	|- ( ph -> ( F : A --> B <-> F : C --> D ) )