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Metamath Proof Explorer

Theorem pm5.74ri

Description: Distribution of implication over biconditional (reverse inference form). (Contributed by NM, 1-Aug-1994)

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

Proof

Step Hyp Ref Expression
1 pm5.74ri.1 
 |-  ( ( ph -> ps ) <-> ( ph -> ch ) )
2 pm5.74 
 |-  ( ( ph -> ( ps <-> ch ) ) <-> ( ( ph -> ps ) <-> ( ph -> ch ) ) )
3 1 2 mpbir 
 |-  ( ph -> ( ps <-> ch ) )