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Theorem ax6evr 2023
 Description: A commuted form of ax6ev 1973. (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 ax6ev 1973 . 2 𝑥 𝑥 = 𝑦
2 equcomiv 2022 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2eximii 1838 1 𝑥 𝑦 = 𝑥
 Colors of variables: wff setvar class Syntax hints:  ∃wex 1781 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016 This theorem depends on definitions:  df-bi 210  df-ex 1782 This theorem is referenced by:  ax7  2024  equvinva  2038  ax12v2  2181  19.8a  2182  axc11n  2450  mo4  2651  eu6lem  2659  axprlem3  5314  relopabi  5682  relop  5709  bj-ax6e  34028  axc11n11r  34044  wl-spae  34838  sn-axprlem3  39283
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