Theorem ax6evr 2016

Description: A commuted form of ax6ev 1970. (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 1970	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2015	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1838	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009

This theorem depends on definitions:  df-bi 207  df-ex 1781

This theorem is referenced by:  ax7  2017  equvinva  2031  ax12v2  2182  19.8a  2184  axc11n  2426  mo4  2561  eu6lem  2568  axprlem3OLD  5366  dfid2  5513  relopabi  5762  relop  5790  bj-ax6e  36708  axc11n11r  36723  bj-dfid2ALT  37105  wl-spae  37561  sn-axprlem3  42256  ormkglobd  46919