Theorem feqmptd

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

	Ref	Expression
Hypothesis	feqmptd.1	$$⊢\phi \to F:A⟶B$$
Assertion	feqmptd	$$⊢\phi \to F=\left(x\in A⟼F\left(x\right)\right)$$

Proof

Step	Hyp	Ref	Expression
1		feqmptd.1	$$⊢\phi \to F:A⟶B$$
2	1	ffnd	$$⊢\phi \to FFnA$$
3		dffn5	$$⊢FFnA\leftrightarrow F=\left(x\in A⟼F\left(x\right)\right)$$
4	2 3	sylib	$$⊢\phi \to F=\left(x\in A⟼F\left(x\right)\right)$$