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Metamath Proof Explorer

Theorem ala1

Description: Add an antecedent in a universally quantified formula. (Contributed by BJ, 6-Oct-2018)

Ref Expression
Assertion ala1 
|- ( A. x ph -> A. x ( ps -> ph ) )

Proof

Step Hyp Ref Expression
1 ax-1 
 |-  ( ph -> ( ps -> ph ) )
2 1 alimi 
 |-  ( A. x ph -> A. x ( ps -> ph ) )