Theorem pm4.44 601

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 400	. 2 |- ( ph -> ( ph \/ ( ph /\ ps ) ) )
2		id 22	. . 3 |- ( ph -> ph )
3		simpl 473	. . 3 |- ( ( ph /\ ps ) -> ph )
4	2, 3	jaoi 394	. 2 |- ( ( ph \/ ( ph /\ ps ) ) -> ph )
5	1, 4	impbii 199	1 |- ( ph <-> ( ph \/ ( ph /\ ps ) ) )

Syntax hints:   <-> wb 196   \/ wo 383   /\ wa 384

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 197  df-or 385  df-an 386

This theorem is referenced by: (None)