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Theorem ax6evr 1679
 Description: A commuted form of a9ev 1673. 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 𝑥 𝑦 = 𝑥
Distinct variable group:   𝑥,𝑦

Proof of Theorem ax6evr
StepHypRef Expression
1 a9ev 1673 . 2 𝑥 𝑥 = 𝑦
2 equcomi 1678 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2eximii 1578 1 𝑥 𝑦 = 𝑥
 Colors of variables: wff set class Syntax hints:  ∃wex 1469 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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1481  ax-4 1487  ax-17 1503  ax-i9 1507  ax-ial 1511 This theorem depends on definitions:  df-bi 116 This theorem is referenced by: (None)
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