Theorem ax6evr 2015

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

Step	Hyp	Ref	Expression
1		ax6ev 1969	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2014	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1837	1 ⊢ ∃𝑥 𝑦 = 𝑥

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 2008

This theorem depends on definitions:  df-bi 207  df-ex 1780

This theorem is referenced by:  ax7  2016  equvinva  2030  ax12v2  2180  19.8a  2182  axc11n  2425  mo4  2560  eu6lem  2567  axprlem3OLD  5386  dfid2  5538  relopabi  5788  relop  5817  bj-ax6e  36663  axc11n11r  36678  bj-dfid2ALT  37060  wl-spae  37516  sn-axprlem3  42212  ormkglobd  46880