Theorem pm4.44 696

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 633	. 2 |- ( ph -> ( ph \/ ( ph /\ ps ) ) )
2		id 19	. . 3 |- ( ph -> ph )
3		simpl 102	. . 3 |- ( ( ph /\ ps ) -> ph )
4	2, 3	jaoi 636	. 2 |- ( ( ph \/ ( ph /\ ps ) ) -> ph )
5	1, 4	impbii 117	1 |- ( ph <-> ( ph \/ ( ph /\ ps ) ) )

Syntax hints:   /\ wa 97   <-> wb 98   \/ wo 629

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-io 630

This theorem depends on definitions:  df-bi 110

This theorem is referenced by: (None)