Theorem nfdisj1

Description: Bound-variable hypothesis builder for disjoint collection. (Contributed by Mario Carneiro, 14-Nov-2016)

	Ref	Expression
Assertion	nfdisj1	$$⊢Ⅎx\underset{x\in A}{Disj}B$$

Proof

Step	Hyp	Ref	Expression
1		df-disj	$$⊢\underset{x\in A}{Disj}B\leftrightarrow \forall y{\exists }^{*}x\in Ay\in B$$
2		nfrmo1	$$⊢Ⅎx{\exists }^{*}x\in Ay\in B$$
3	2	nfal	$$⊢Ⅎx\forall y{\exists }^{*}x\in Ay\in B$$
4	1 3	nfxfr	$$⊢Ⅎx\underset{x\in A}{Disj}B$$