Theorem feqmptd

Description: Deduction form of dffn5 . (Contributed by Mario Carneiro, 8-Jan-2015)

	Ref	Expression
Hypothesis	feqmptd.1	|- ( ph -> F : A --> B )
Assertion	feqmptd	|- ( ph -> F = ( x e. A |-> ( F ` x ) ) )

Proof

Step	Hyp	Ref	Expression
1		feqmptd.1	|- ( ph -> F : A --> B )
2	1	ffnd	|- ( ph -> F Fn A )
3		dffn5	|- ( F Fn A <-> F = ( x e. A |-> ( F ` x ) ) )
4	2 3	sylib	|- ( ph -> F = ( x e. A |-> ( F ` x ) ) )