Theorem pm5.55 939

Description: Theorem *5.55 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 20-Jan-2013.)

Assertion

Ref	Expression
pm5.55	|- ( ( ( ph \/ ps ) <-> ph ) \/ ( ( ph \/ ps ) <-> ps ) )

Proof of Theorem pm5.55

Step	Hyp	Ref	Expression
1		biort 938	. . . . 5 |- ( ph -> ( ph <-> ( ph \/ ps ) ) )
2	1	bicomd 213	. . . 4 |- ( ph -> ( ( ph \/ ps ) <-> ph ) )
3		biorf 420	. . . . 5 |- ( -. ph -> ( ps <-> ( ph \/ ps ) ) )
4	3	bicomd 213	. . . 4 |- ( -. ph -> ( ( ph \/ ps ) <-> ps ) )
5	2, 4	nsyl4 156	. . 3 |- ( -. ( ( ph \/ ps ) <-> ps ) -> ( ( ph \/ ps ) <-> ph ) )
6	5	con1i 144	. 2 |- ( -. ( ( ph \/ ps ) <-> ph ) -> ( ( ph \/ ps ) <-> ps ) )
7	6	orri 391	1 |- ( ( ( ph \/ ps ) <-> ph ) \/ ( ( ph \/ ps ) <-> ps ) )

Syntax hints:   -. wn 3   <-> wb 196   \/ wo 383

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

This theorem is referenced by: (None)