Theorem pm4.42 926

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

Assertion

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

Proof of Theorem pm4.42

Step	Hyp	Ref	Expression
1		dedlema 920	. 2 |- (ps -> (ph <-> ((ph /\ ps) \/ (ph /\ -. ps))))
2		dedlemb 921	. 2 |- (-. ps -> (ph <-> ((ph /\ ps) \/ (ph /\ -. ps))))
3	1, 2	pm2.61i 156	1 |- (ph <-> ((ph /\ ps) \/ (ph /\ -. ps)))

Syntax hints:  -. wn 3   <-> wb 176   \/ wo 357   /\ wa 358

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360

This theorem is referenced by:  inundif  3629