Theorem ax13dgen1

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

	Ref	Expression
Assertion	ax13dgen1	$$⊢\neg x=x\to \left(x=z\to \forall xx=z\right)$$

Proof

Step	Hyp	Ref	Expression
1		equid	$$⊢x=x$$
2	1	pm2.24i	$$⊢\neg x=x\to \left(x=z\to \forall xx=z\right)$$