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

Metamath Proof Explorer

Theorem equcomi

Description: Commutative law for equality. Equality is a symmetric relation. Lemma 3 of KalishMontague p. 85. See also Lemma 7 of Tarski p. 69. (Contributed by NM, 10-Jan-1993) (Revised by NM, 9-Apr-2017)

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

Proof

Step	Hyp	Ref	Expression
1		equid	$⊢ x = x$
2		ax7	$⊢ x = y \to (x = x \to y = x)$
3	1 2	mpi	$⊢ x = y \to y = x$