Theorem wl-speqv

Description: Under the assumption -. x = y a specialized version of sp is provable from Tarski's FOL and ax13v only. Note that this reverts the implication in ax13lem1 , so in fact ( -. x = y -> ( A. x z = y <-> z = y ) ) holds. (Contributed by Wolf Lammen, 17-Apr-2021)

	Ref	Expression
Assertion	wl-speqv	$$⊢\neg x=y\to \left(\forall xz=y\to z=y\right)$$

Proof

Step	Hyp	Ref	Expression
1		19.2	$$⊢\forall xz=y\to \exists xz=y$$
2		ax13lem2	$$⊢\neg x=y\to \left(\exists xz=y\to z=y\right)$$
3	1 2	syl5	$$⊢\neg x=y\to \left(\forall xz=y\to z=y\right)$$