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

Metamath Proof Explorer

Theorem equcomd

Description: Deduction form of equcom , symmetry of equality. For the versions for classes, see eqcom and eqcomd . (Contributed by BJ, 6-Oct-2019)

		Ref	Expression
	Hypothesis	equcomd.1	$⊢ φ \to x = y$
	Assertion	equcomd	$⊢ φ \to y = x$

Proof

Step	Hyp	Ref	Expression
1		equcomd.1	$⊢ φ \to x = y$
2		equcom	$⊢ x = y \leftrightarrow y = x$
3	1 2	sylib	$⊢ φ \to y = x$