Theorem ax6evr 1751

Description: A commuted form of a9ev 1743. 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 1743	. 2 |- E. x x = y
2		equcomi 1750	. 2 |- ( x = y -> y = x )
3	1, 2	eximii 1648	1 |- E. x y = x

Syntax hints:   E.wex 1538

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)