Theorem ax6evr 1727

Description: A commuted form of a9ev 1719. 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 1719	. 2 |- E. x x = y
2		equcomi 1726	. 2 |- ( x = y -> y = x )
3	1, 2	eximii 1624	1 |- E. x y = x

Syntax hints:   E.wex 1514

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)