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Metamath Proof Explorer

Theorem pm5.32d

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 29-Oct-1996)

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

Proof

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