Theorem equeucl

Description: Equality is a left-Euclidean binary relation. (Right-Euclideanness is stated in ax-7 .) Curried (exported) form of equtr2 . (Contributed by BJ, 11-Apr-2021)

	Ref	Expression
Assertion	equeucl	$$⊢x=z\to \left(y=z\to x=y\right)$$

Proof

Step	Hyp	Ref	Expression
1		equeuclr	$$⊢y=z\to \left(x=z\to x=y\right)$$
2	1	com12	$$⊢x=z\to \left(y=z\to x=y\right)$$