Theorem pm4.44 560

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

Assertion

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

Proof of Theorem pm4.44

Step	Hyp	Ref	Expression
1		orc 374	. 2 |- (ph -> (ph \/ (ph /\ ps)))
2		id 19	. . 3 |- (ph -> ph)
3		simpl 443	. . 3 |- ((ph /\ ps) -> ph)
4	2, 3	jaoi 368	. 2 |- ((ph \/ (ph /\ ps)) -> ph)
5	1, 4	impbii 180	1 |- (ph <-> (ph \/ (ph /\ ps)))

Syntax hints:   <-> 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: (None)