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 ) ) )