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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 -> ph )
Assertion equcoms 
|- ( y = x -> ph )

Proof

Step Hyp Ref Expression
1 equcoms.1 
 |-  ( x = y -> ph )
2 equcomi 
 |-  ( y = x -> x = y )
3 2 1 syl 
 |-  ( y = x -> ph )