Theorem ax6evr 2022

Description: A commuted form of ax6ev 1972. (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 1972	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2021	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1838	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 1911  ax-6 1970  ax-7 2015

This theorem depends on definitions:  df-bi 210  df-ex 1782

This theorem is referenced by:  ax7  2023  equvinva  2037  ax12v2  2177  19.8a  2178  axc11n  2437  mo4  2625  eu6lem  2633  axprlem3  5291  relopabi  5658  relop  5685  bj-ax6e  34114  axc11n11r  34130  wl-spae  34926  sn-axprlem3  39401