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Metamath Proof Explorer

Theorem equtr2

Description: Equality is a left-Euclidean binary relation. Uncurried (imported) form of equeucl . (Contributed by NM, 12-Aug-1993) (Proof shortened by Andrew Salmon, 25-May-2011) (Proof shortened by BJ, 11-Apr-2021)

		Ref	Expression
	Assertion	equtr2	$⊢ (x = z \land y = z) \to x = y$

Proof

Step	Hyp	Ref	Expression
1		equeucl	$⊢ x = z \to (y = z \to x = y)$
2	1	imp	$⊢ (x = z \land y = z) \to x = y$