Theorem nfmpt1

Description: Bound-variable hypothesis builder for the maps-to notation. (Contributed by FL, 17-Feb-2008)

	Ref	Expression
Assertion	nfmpt1	$$⊢\underset{\_}{Ⅎ}x\left(x\in A⟼B\right)$$

Proof

Step	Hyp	Ref	Expression
1		df-mpt	$$⊢\left(x\in A⟼B\right)=\left\{⟨x,z⟩|\left(x\in A\wedge z=B\right)\right\}$$
2		nfopab1	$$⊢\underset{\_}{Ⅎ}x\left\{⟨x,z⟩|\left(x\in A\wedge z=B\right)\right\}$$
3	1 2	nfcxfr	$$⊢\underset{\_}{Ⅎ}x\left(x\in A⟼B\right)$$