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Metamath Proof Explorer

Theorem pm5.32da

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 9-Dec-2006)

Ref Expression
Hypothesis pm5.32da.1 
|- ( ( ph /\ ps ) -> ( ch <-> th ) )
Assertion pm5.32da 
|- ( ph -> ( ( ps /\ ch ) <-> ( ps /\ th ) ) )

Proof

Step Hyp Ref Expression
1 pm5.32da.1 
 |-  ( ( ph /\ ps ) -> ( ch <-> th ) )
2 1 ex 
 |-  ( ph -> ( ps -> ( ch <-> th ) ) )
3 2 pm5.32d 
 |-  ( ph -> ( ( ps /\ ch ) <-> ( ps /\ th ) ) )