Metamath Proof Explorer


Theorem equeuclr

Description: Commuted version of equeucl (equality is left-Euclidean). (Contributed by BJ, 12-Apr-2021)

Ref Expression
Assertion equeuclr ( 𝑥 = 𝑧 → ( 𝑦 = 𝑧 → 𝑦 = 𝑥 ) )

Proof

Step Hyp Ref Expression
1 equtrr ⊢ ( 𝑧 = 𝑥 → ( 𝑦 = 𝑧 → 𝑦 = 𝑥 ) )
2 1 equcoms ⊢ ( 𝑥 = 𝑧 → ( 𝑦 = 𝑧 → 𝑦 = 𝑥 ) )