Theorem feq23

Description: Equality theorem for functions. (Contributed by FL, 14-Jul-2007) (Proof shortened by Andrew Salmon, 17-Sep-2011)

	Ref	Expression
Assertion	feq23	$$⊢\left(A=C\wedge B=D\right)\to \left(F:A⟶B\leftrightarrow F:C⟶D\right)$$

Proof

Step	Hyp	Ref	Expression
1		feq2	$$⊢A=C\to \left(F:A⟶B\leftrightarrow F:C⟶B\right)$$
2		feq3	$$⊢B=D\to \left(F:C⟶B\leftrightarrow F:C⟶D\right)$$
3	1 2	sylan9bb	$$⊢\left(A=C\wedge B=D\right)\to \left(F:A⟶B\leftrightarrow F:C⟶D\right)$$