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Metamath Proof Explorer

Theorem pm5.6

Description: Conjunction in antecedent versus disjunction in consequent. Theorem *5.6 of WhiteheadRussell p. 125. (Contributed by NM, 8-Jun-1994)

Ref Expression
Assertion pm5.6 
|- ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( ps \/ ch ) ) )

Proof

Step Hyp Ref Expression
1 impexp 
 |-  ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( -. ps -> ch ) ) )
2 df-or 
 |-  ( ( ps \/ ch ) <-> ( -. ps -> ch ) )
3 2 imbi2i 
 |-  ( ( ph -> ( ps \/ ch ) ) <-> ( ph -> ( -. ps -> ch ) ) )
4 1 3 bitr4i 
 |-  ( ( ( ph /\ -. ps ) -> ch ) <-> ( ph -> ( ps \/ ch ) ) )