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Theorem ax6evr 1666
Description: A commuted form of a9ev 1660. 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 1660 . 2  |-  E. x  x  =  y
2 equcomi 1665 . 2  |-  ( x  =  y  ->  y  =  x )
31, 2eximii 1566 1  |-  E. x  y  =  x
Colors of variables: wff set class
Syntax hints:   E.wex 1453
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1408  ax-gen 1410  ax-ie1 1454  ax-ie2 1455  ax-8 1467  ax-4 1472  ax-17 1491  ax-i9 1495  ax-ial 1499
This theorem depends on definitions:  df-bi 116
This theorem is referenced by: (None)
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