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Metamath Proof Explorer

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 → y = z → x = y

Proof

Step Hyp Ref Expression
1 equeuclr ⊢ y = z → x = z → x = y
2 1 com12 ⊢ x = z → y = z → x = y