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Metamath Proof Explorer

Theorem jao1i

Description: Add a disjunct in the antecedent of an implication. (Contributed by Rodolfo Medina, 24-Sep-2010)

Ref Expression
Hypothesis jao1i.1 
|- ( ps -> ( ch -> ph ) )
Assertion jao1i 
|- ( ( ph \/ ps ) -> ( ch -> ph ) )

Proof

Step Hyp Ref Expression
1 jao1i.1 
 |-  ( ps -> ( ch -> ph ) )
2 ax-1 
 |-  ( ph -> ( ch -> ph ) )
3 2 1 jaoi 
 |-  ( ( ph \/ ps ) -> ( ch -> ph ) )