Theorem feq2d

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

	Ref	Expression
Hypothesis	feq2d.1	|- ( ph -> A = B )
Assertion	feq2d	|- ( ph -> ( F : A --> C <-> F : B --> C ) )

Proof

Step	Hyp	Ref	Expression
1		feq2d.1	|- ( ph -> A = B )
2		feq2	|- ( A = B -> ( F : A --> C <-> F : B --> C ) )
3	1 2	syl	|- ( ph -> ( F : A --> C <-> F : B --> C ) )