Theorem ax6evr 2038

Description: A commuted form of ax6ev 1992. (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 1992	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2037	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1860	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1802

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1818  ax-4 1832  ax-5 1933  ax-6 1990  ax-7 2031

This theorem depends on definitions:  df-bi 210  df-ex 1803

This theorem is referenced by:  ax7  2039  equvinva  2053  ax12v2  2217  19.8a  2219  axc11n  2460  mo4  2596  eu6lem  2603  axprlem3OLD  5390  dfid2  5548  relopabi  5799  relop  5826  bj-ax6e  37147  axc11n11r  37165  bj-dfid2ALT  37557  wl-spae  38031  sn-axprlem3  42844  ormkglobd  47450