Theorem feq23d

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

	Ref	Expression
Hypotheses	feq23d.1	$$⊢\phi \to A=C$$
	feq23d.2	$$⊢\phi \to B=D$$
Assertion	feq23d	$$⊢\phi \to \left(F:A⟶B\leftrightarrow F:C⟶D\right)$$

Proof

Step	Hyp	Ref	Expression
1		feq23d.1	$$⊢\phi \to A=C$$
2		feq23d.2	$$⊢\phi \to B=D$$
3		eqidd	$$⊢\phi \to F=F$$
4	3 1 2	feq123d	$$⊢\phi \to \left(F:A⟶B\leftrightarrow F:C⟶D\right)$$