Theorem wl-ax11-lem7

Description: Lemma. (Contributed by Wolf Lammen, 30-Jun-2019)

	Ref	Expression
Assertion	wl-ax11-lem7	$$⊢\forall x\left(\neg \forall xx=y\wedge \phi \right)\leftrightarrow \left(\neg \forall xx=y\wedge \forall x\phi \right)$$

Proof

Step	Hyp	Ref	Expression
1		nfna1	$$⊢Ⅎx\neg \forall xx=y$$
2	1	19.28	$$⊢\forall x\left(\neg \forall xx=y\wedge \phi \right)\leftrightarrow \left(\neg \forall xx=y\wedge \forall x\phi \right)$$