Theorem ax6evr 2045

Description: A commuted form of ax6ev 1999. (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 1999	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2044	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1867	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1809

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038

This theorem depends on definitions:  df-bi 210  df-ex 1810

This theorem is referenced by:  ax7  2046  equvinva  2060  ax12v2  2215  19.8a  2217  axc11n  2458  mo4  2594  eu6lem  2601  axprlem3OLD  5402  dfid2  5560  relopabi  5811  relop  5838  bj-ax6e  37271  axc11n11r  37289  bj-dfid2ALT  37682  wl-spae  38157  sn-axprlem3  42970  ormkglobd  47574