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Metamath Proof Explorer

Theorem pm5.74rd

Description: Distribution of implication over biconditional (deduction form). (Contributed by NM, 19-Mar-1997)

Ref Expression
Hypothesis pm5.74rd.1 
|- ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )
Assertion pm5.74rd 
|- ( ph -> ( ps -> ( ch <-> th ) ) )

Proof

Step Hyp Ref Expression
1 pm5.74rd.1 
 |-  ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )
2 pm5.74 
 |-  ( ( ps -> ( ch <-> th ) ) <-> ( ( ps -> ch ) <-> ( ps -> th ) ) )
3 1 2 sylibr 
 |-  ( ph -> ( ps -> ( ch <-> th ) ) )