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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
StepHypRef Expression
1 a9ev 1708 . 2  |-  E. x  x  =  y
2 equcomi 1715 . 2  |-  ( x  =  y  ->  y  =  x )
31, 2eximii 1613 1  |-  E. x  y  =  x
Colors of variables: wff set class
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)
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