Theorem ax6evr 1939

Description: A commuted form of ax6ev 1887. (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 1887	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 1938	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1761	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1701

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1719  ax-4 1734  ax-5 1836  ax-6 1885  ax-7 1932

This theorem depends on definitions:  df-bi 197  df-ex 1702

This theorem is referenced by:  ax7  1940  equviniva  1957  ax12v2  2046  ax12vOLD  2047  19.8a  2049  axc11n  2306  euequ1  2475  relopabi  5215  relop  5242  bj-ax6e  32348  axc11n11r  32368  wl-spae  32977