Theorem wl-aetr

Description: A transitive law for variable identifying expressions. (Contributed by Wolf Lammen, 30-Jun-2019)

	Ref	Expression
Assertion	wl-aetr	$$⊢\forall xx=y\to \left(\forall xx=z\to \forall yy=z\right)$$

Proof

Step	Hyp	Ref	Expression
1		ax7	$$⊢x=y\to \left(x=z\to y=z\right)$$
2	1	al2imi	$$⊢\forall xx=y\to \left(\forall xx=z\to \forall xy=z\right)$$
3		axc11	$$⊢\forall xx=y\to \left(\forall xy=z\to \forall yy=z\right)$$
4	2 3	syld	$$⊢\forall xx=y\to \left(\forall xx=z\to \forall yy=z\right)$$