Theorem ax6evr 2014

Description: A commuted form of ax6ev 1969. (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 1969	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomiv 2013	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1835	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1777

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007

This theorem depends on definitions:  df-bi 207  df-ex 1778

This theorem is referenced by:  ax7  2015  equvinva  2029  ax12v2  2180  19.8a  2182  axc11n  2434  mo4  2569  eu6lem  2576  axprlem3  5443  dfid2  5595  relopabi  5846  relop  5875  bj-ax6e  36634  axc11n11r  36649  bj-dfid2ALT  37031  wl-spae  37475  sn-axprlem3  42210