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Metamath Proof Explorer

Theorem equcoms

Description: An inference commuting equality in antecedent. Used to eliminate the need for a syllogism. (Contributed by NM, 10-Jan-1993)

Ref Expression
Hypothesis equcoms.1 ⊢ ( 𝑥 = 𝑦 → 𝜑 )
Assertion equcoms ( 𝑦 = 𝑥 → 𝜑 )

Proof

Step Hyp Ref Expression
1 equcoms.1 ⊢ ( 𝑥 = 𝑦 → 𝜑 )
2 equcomi ⊢ ( 𝑦 = 𝑥 → 𝑥 = 𝑦 )
3 2 1 syl ⊢ ( 𝑦 = 𝑥 → 𝜑 )