Theorem ax6evr 1753

Description: A commuted form of a9ev 1745. 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 1745	. 2 |- E. x x = y
2		equcomi 1752	. 2 |- ( x = y -> y = x )
3	1, 2	eximii 1650	1 |- E. x y = x

Syntax hints:   E.wex 1540

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)