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Metamath Proof Explorer

Theorem alcoms

Description: Swap quantifiers in an antecedent. (Contributed by NM, 11-May-1993)

Ref Expression
Hypothesis alcoms.1 
|- ( A. x A. y ph -> ps )
Assertion alcoms 
|- ( A. y A. x ph -> ps )

Proof

Step Hyp Ref Expression
1 alcoms.1 
 |-  ( A. x A. y ph -> ps )
2 ax-11 
 |-  ( A. y A. x ph -> A. x A. y ph )
3 2 1 syl 
 |-  ( A. y A. x ph -> ps )