Theorem ax6evr 1716

Description: A commuted form of a9ev 1708. The naming reflects how axioms were numbered in the Metamath Proof Explorer as of 2020 (a numbering which we eventually plan to adopt here too, but until this happens everywhere only some theorems will have it). (Contributed by BJ, 7-Dec-2020.)

Assertion

Ref	Expression
ax6evr	|- E. x y = x

Distinct variable group:   x, y

Proof of Theorem ax6evr

Step	Hyp	Ref	Expression
1		a9ev 1708	. 2 |- E. x x = y
2		equcomi 1715	. 2 |- ( x = y -> y = x )
3	1, 2	eximii 1613	1 |- E. x y = x

Syntax hints:   E.wex 1503

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)