Theorem ax6evr 2095

Description: A commuted form of ax6ev 2054. (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 2054	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2094	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1911	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1851

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1869  ax-4 1884  ax-5 1986  ax-6 2052  ax-7 2088

This theorem depends on definitions:  df-bi 197  df-ex 1852

This theorem is referenced by:  ax7  2096  equviniva  2111  ax12v2  2196  19.8a  2197  axc11n  2449  euequ1  2611  relopabi  5399  relop  5426  bj-ax6e  32957  axc11n11r  32977  wl-spae  33617