Theorem nfsb2

Description: Bound-variable hypothesis builder for substitution. Usage of this theorem is discouraged because it depends on ax-13 . (Contributed by Mario Carneiro, 4-Oct-2016) (New usage is discouraged.)

	Ref	Expression
Assertion	nfsb2	$$⊢\neg \forall xx=y\to Ⅎx\left[y/x\right]\phi$$

Proof

Step	Hyp	Ref	Expression
1		nfna1	$$⊢Ⅎx\neg \forall xx=y$$
2		hbsb2	$$⊢\neg \forall xx=y\to \left(\left[y/x\right]\phi \to \forall x\left[y/x\right]\phi \right)$$
3	1 2	nf5d	$$⊢\neg \forall xx=y\to Ⅎx\left[y/x\right]\phi$$