Theorem ax6evr 1929

Description: A commuted form of ax6ev 1877. (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 1877	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 1928	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1754	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1695

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1713  ax-4 1728  ax-5 1827  ax-6 1875  ax-7 1922

This theorem depends on definitions:  df-bi 196  df-ex 1696

This theorem is referenced by:  ax7  1930  equviniva  1947  ax12v2  2036  ax12vOLD  2037  19.8a  2039  axc11n  2295  euequ1  2464  relopabi  5167  relop  5194  bj-ax6e  31842  axc11n11r  31860  wl-spae  32485