Theorem ax13dgen3

Description: Degenerate instance of ax-13 where bundled variables y and z have a common substitution. Uses only Tarski's FOL axiom schemes. (Contributed by NM, 13-Apr-2017)

	Ref	Expression
Assertion	ax13dgen3	$$⊢\neg x=y\to \left(y=y\to \forall xy=y\right)$$

Proof

Step	Hyp	Ref	Expression
1		equid	$$⊢y=y$$
2	1	ax-gen	$$⊢\forall xy=y$$
3	2	2a1i	$$⊢\neg x=y\to \left(y=y\to \forall xy=y\right)$$