This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem equcomiv

Description: Weaker form of equcomi with a disjoint variable condition on x , y . This is an intermediate step and equcomi is fully recovered later. (Contributed by BJ, 7-Dec-2020)

		Ref	Expression
	Assertion	equcomiv	$⊢ x = y \to y = x$

Proof

Step	Hyp	Ref	Expression
1		equid	$⊢ x = x$
2		ax7v2	$⊢ x = y \to (x = x \to y = x)$
3	1 2	mpi	$⊢ x = y \to y = x$