Theorem ax6evr 2050

Description: A commuted form of ax6ev 2004. (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 2004	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2049	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1870	1 ⊢ ∃𝑥 𝑦 = 𝑥

This proof depends on syntax axioms:  ∃wex 1812

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1945  ax-6 2002  ax-7 2043

This proof depends on definitions:  df-bi 210  df-ex 1813

This theorem is used by:  ax7  2051  equvinva  2065  ax12v2  2218  19.8a  2221  axc11n  2458  mo4  2594  eu6lem  2601  dfid2  5553  relopabi  5806  relopabiOLD  5807  relop  5835  bj-ax6e  37758  axc11n11r  37776  bj-dfid2ALT  38184  wl-spae  38658  cbvex2ivw  43466  sn-axprlem3  43476  ormkglobd  48102