Theorem ax6evr 2047

Description: A commuted form of ax6ev 2001. (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 2001	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2046	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1869	1 ⊢ ∃𝑥 𝑦 = 𝑥

This proof depends on syntax axioms:  ∃wex 1811

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1827  ax-4 1841  ax-5 1942  ax-6 1999  ax-7 2040

This proof depends on definitions:  df-bi 210  df-ex 1812

This theorem is used by:  ax7  2048  equvinva  2062  ax12v2  2214  19.8a  2217  axc11n  2455  mo4  2591  eu6lem  2598  dfid2  5547  relopabi  5799  relop  5827  bj-ax6e  37660  axc11n11r  37678  coi1in  38054  bj-dfid2ALT  38073  wl-spae  38547  sn-axprlem3  43366  ormkglobd  47981