Theorem ax6evr 2114

Description: A commuted form of ax6ev 2074. (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 2074	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2113	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1932	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1891  ax-4 1905  ax-5 2006  ax-6 2072  ax-7 2107

This theorem depends on definitions:  df-bi 199  df-ex 1876

This theorem is referenced by:  ax7  2115  equvinva  2131  ax12v2  2215  19.8a  2216  axc11n  2431  eu6  2611  eu6OLD  2612  euequ  2633  relopabi  5447  relop  5474  elridOLD  5668  bj-ax6e  33150  axc11n11r  33170  wl-spae  33789