Theorem bj-ax6elem1

Description: Lemma for bj-ax6e . (Contributed by BJ, 22-Dec-2020) (Proof modification is discouraged.)

	Ref	Expression
Assertion	bj-ax6elem1	$$⊢\neg \forall xx=y\to \left(y=z\to \forall xy=z\right)$$

Proof

Step	Hyp	Ref	Expression
1		axc9	$$⊢\neg \forall xx=y\to \left(\neg \forall xx=z\to \left(y=z\to \forall xy=z\right)\right)$$
2		axc16	$$⊢\forall xx=z\to \left(y=z\to \forall xy=z\right)$$
3	1 2	pm2.61d2	$$⊢\neg \forall xx=y\to \left(y=z\to \forall xy=z\right)$$