Theorem ax6evr 2010

Description: A commuted form of ax6ev 1965. (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 1965	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2009	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1831	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1773

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003

This theorem depends on definitions:  df-bi 206  df-ex 1774

This theorem is referenced by:  ax7  2011  equvinva  2025  ax12v2  2165  19.8a  2166  axc11n  2417  mo4  2552  eu6lem  2559  axprlem3  5413  dfid2  5566  relopabi  5812  relop  5840  bj-ax6e  36035  axc11n11r  36051  bj-dfid2ALT  36436  wl-spae  36880  sn-axprlem3  41527