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Metamath Proof Explorer

Theorem pm4.44

Description: Theorem *4.44 of WhiteheadRussell p. 119. (Contributed by NM, 3-Jan-2005)

Ref Expression
Assertion pm4.44 
|- ( ph <-> ( ph \/ ( ph /\ ps ) ) )

Proof

Step Hyp Ref Expression
1 orc 
 |-  ( ph -> ( ph \/ ( ph /\ ps ) ) )
2 id 
 |-  ( ph -> ph )
3 simpl 
 |-  ( ( ph /\ ps ) -> ph )
4 2 3 jaoi 
 |-  ( ( ph \/ ( ph /\ ps ) ) -> ph )
5 1 4 impbii 
 |-  ( ph <-> ( ph \/ ( ph /\ ps ) ) )