Theorem ax6evr 2011

Description: A commuted form of ax6ev 1966. (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 1966	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2010	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1833	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1775

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1791  ax-4 1805  ax-5 1907  ax-6 1964  ax-7 2004

This theorem depends on definitions:  df-bi 207  df-ex 1776

This theorem is referenced by:  ax7  2012  equvinva  2026  ax12v2  2176  19.8a  2178  axc11n  2428  mo4  2563  eu6lem  2570  axprlem3OLD  5433  dfid2  5584  relopabi  5834  relop  5863  bj-ax6e  36650  axc11n11r  36665  bj-dfid2ALT  37047  wl-spae  37501  sn-axprlem3  42234