Theorem ax6evr 2017

Description: A commuted form of ax6ev 1971. (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 1971	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2016	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1839	1 ⊢ ∃𝑥 𝑦 = 𝑥

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 1969  ax-7 2010

This theorem depends on definitions:  df-bi 207  df-ex 1782

This theorem is referenced by:  ax7  2018  equvinva  2032  ax12v2  2187  19.8a  2189  axc11n  2430  mo4  2566  eu6lem  2573  axprlem3OLD  5371  dfid2  5528  relopabi  5778  relop  5805  bj-ax6e  36962  axc11n11r  36980  bj-dfid2ALT  37372  wl-spae  37846  sn-axprlem3  42659  ormkglobd  47305