Theorem ax6evr 2019

Description: A commuted form of ax6ev 1974. (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 1974	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2018	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1840	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1783

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1799  ax-4 1813  ax-5 1914  ax-6 1972  ax-7 2012

This theorem depends on definitions:  df-bi 206  df-ex 1784

This theorem is referenced by:  ax7  2020  equvinva  2034  ax12v2  2175  19.8a  2176  axc11n  2426  mo4  2566  eu6lem  2573  axprlem3  5343  dfid2  5482  relopabi  5721  relop  5748  bj-ax6e  34776  axc11n11r  34792  bj-dfid2ALT  35163  wl-spae  35607  sn-axprlem3  40114