Theorem nfsb2ALT

Description: Alternate version of nfsb2 . (Contributed by Mario Carneiro, 4-Oct-2016) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypothesis	dfsb1.p3	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
Assertion	nfsb2ALT	$$⊢\neg \forall xx=y\to Ⅎx\theta$$

Proof

Step	Hyp	Ref	Expression
1		dfsb1.p3	$$⊢\theta \leftrightarrow \left(\left(x=y\to \phi \right)\wedge \exists x\left(x=y\wedge \phi \right)\right)$$
2		nfna1	$$⊢Ⅎx\neg \forall xx=y$$
3	1	hbsb2ALT	$$⊢\neg \forall xx=y\to \left(\theta \to \forall x\theta \right)$$
4	2 3	nf5d	$$⊢\neg \forall xx=y\to Ⅎx\theta$$