Theorem ax6evr 2022

Description: A commuted form of ax6ev 1976. (Contributed by BJ, 7-Dec-2020.)

Assertion

Ref	Expression
ax6evr	⊢ ∃𝑥 𝑦 = 𝑥

Distinct variable group:   𝑥,𝑦

Proof of Theorem ax6evr

Step	Hyp	Ref	Expression
1		ax6ev 1976	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2021	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1844	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1786

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015

This theorem depends on definitions:  df-bi 208  df-ex 1787

This theorem is referenced by:  ax7  2023  equvinva  2037  ax12v2  2191  19.8a  2193  axc11n  2434  mo4  2570  eu6lem  2577  axprlem3OLD  5365  dfid2  5522  relopabi  5772  relop  5799  bj-ax6e  37015  axc11n11r  37033  bj-dfid2ALT  37425  wl-spae  37899  sn-axprlem3  42712  ormkglobd  47327