Theorem ax6evr 2034

Description: A commuted form of ax6ev 1988. (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 1988	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2033	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1856	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1798

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1814  ax-4 1828  ax-5 1929  ax-6 1986  ax-7 2027

This theorem depends on definitions:  df-bi 209  df-ex 1799

This theorem is referenced by:  ax7  2035  equvinva  2049  ax12v2  2213  19.8a  2215  axc11n  2456  mo4  2592  eu6lem  2599  axprlem3OLD  5383  dfid2  5540  relopabi  5791  relop  5818  bj-ax6e  37100  axc11n11r  37118  bj-dfid2ALT  37510  wl-spae  37984  sn-axprlem3  42797  ormkglobd  47411