MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  ax6evr Structured version   Visualization version   GIF version

Theorem ax6evr 2014
Description: A commuted form of ax6ev 1969. (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 1969 . 2 𝑥 𝑥 = 𝑦
2 equcomiv 2013 . 2 (𝑥 = 𝑦𝑦 = 𝑥)
31, 2eximii 1837 1 𝑥 𝑦 = 𝑥
Colors of variables: wff setvar class
Syntax hints:  wex 1779
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007
This theorem depends on definitions:  df-bi 207  df-ex 1780
This theorem is referenced by:  ax7  2015  equvinva  2029  ax12v2  2179  19.8a  2181  axc11n  2431  mo4  2566  eu6lem  2573  axprlem3OLD  5428  dfid2  5580  relopabi  5832  relop  5861  bj-ax6e  36669  axc11n11r  36684  bj-dfid2ALT  37066  wl-spae  37522  sn-axprlem3  42256  ormkglobd  46890
  Copyright terms: Public domain W3C validator