Theorem ax6evr 1719

Description: A commuted form of a9ev 1711. 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 1711	. 2 |- E. x x = y
2		equcomi 1718	. 2 |- ( x = y -> y = x )
3	1, 2	eximii 1616	1 |- E. x y = x

Syntax hints:   E.wex 1506

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-8 1518  ax-4 1524  ax-17 1540  ax-i9 1544  ax-ial 1548

This theorem depends on definitions:  df-bi 117

This theorem is referenced by: (None)