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Metamath Proof Explorer

Theorem pm5.74da

Description: Distribution of implication over biconditional (deduction form). Variant of pm5.74d . (Contributed by NM, 4-May-2007)

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

Proof

Step Hyp Ref Expression
1 pm5.74da.1 
 |-  ( ( ph /\ ps ) -> ( ch <-> th ) )
2 1 ex 
 |-  ( ph -> ( ps -> ( ch <-> th ) ) )
3 2 pm5.74d 
 |-  ( ph -> ( ( ps -> ch ) <-> ( ps -> th ) ) )