Theorem ax6evr 1681

Description: A commuted form of a9ev 1675. The naming reflects how axioms were numbered in the Metamath Proof Explorer as of 2020 (a numbering which we eventually plan to adopt here too, but until this happens everywhere only some theorems will have it). (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		a9ev 1675	. 2 ⊢ ∃𝑥 𝑥 = 𝑦
2		equcomi 1680	. 2 ⊢ (𝑥 = 𝑦 → 𝑦 = 𝑥)
3	1, 2	eximii 1581	1 ⊢ ∃𝑥 𝑦 = 𝑥

Syntax hints:  ∃wex 1468

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514

This theorem depends on definitions:  df-bi 116

This theorem is referenced by: (None)