Theorem ax6evr 2018

Description: A commuted form of ax6ev 1973. (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 1973	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2017	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1839	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1782

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1798  ax-4 1812  ax-5 1913  ax-6 1971  ax-7 2011

This theorem depends on definitions:  df-bi 206  df-ex 1783

This theorem is referenced by:  ax7  2019  equvinva  2033  ax12v2  2173  19.8a  2174  axc11n  2426  mo4  2566  eu6lem  2573  axprlem3  5348  dfid2  5491  relopabi  5732  relop  5759  bj-ax6e  34849  axc11n11r  34865  bj-dfid2ALT  35236  wl-spae  35680  sn-axprlem3  40186