Metamath Proof Explorer


Theorem equtr

Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993)

Ref Expression
Assertion equtr ( 𝑥 = 𝑦 → ( 𝑦 = 𝑧𝑥 = 𝑧 ) )

Proof

Step Hyp Ref Expression
1 ax7 ( 𝑦 = 𝑥 → ( 𝑦 = 𝑧𝑥 = 𝑧 ) )
2 1 equcoms ( 𝑥 = 𝑦 → ( 𝑦 = 𝑧𝑥 = 𝑧 ) )