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	$$⊢\left(x=z\wedge y=z\right)\to x=y$$

Proof

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