Metamath Proof Explorer

Theorem pm4.42

Description: Theorem *4.42 of WhiteheadRussell p. 119. See also ifpid . (Contributed by Roy F. Longton, 21-Jun-2005)

Ref Expression
Assertion pm4.42 
|- ( ph <-> ( ( ph /\ ps ) \/ ( ph /\ -. ps ) ) )

Proof

Step Hyp Ref Expression
1 dedlema 
 |-  ( ps -> ( ph <-> ( ( ph /\ ps ) \/ ( ph /\ -. ps ) ) ) )
2 dedlemb 
 |-  ( -. ps -> ( ph <-> ( ( ph /\ ps ) \/ ( ph /\ -. ps ) ) ) )
3 1 2 pm2.61i 
 |-  ( ph <-> ( ( ph /\ ps ) \/ ( ph /\ -. ps ) ) )