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


Step Hyp Ref Expression
1 equcoms.1 x = y φ
2 equcomi y = x x = y
3 2 1 syl y = x φ