Theorem pm5.55 867

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 866	. . . . 5 |- (ph -> (ph <-> (ph \/ ps)))
2	1	bicomd 192	. . . 4 |- (ph -> ((ph \/ ps) <-> ph))
3		biorf 394	. . . . 5 |- (-. ph -> (ps <-> (ph \/ ps)))
4	3	bicomd 192	. . . 4 |- (-. ph -> ((ph \/ ps) <-> ps))
5	2, 4	nsyl4 134	. . 3 |- (-. ((ph \/ ps) <-> ps) -> ((ph \/ ps) <-> ph))
6	5	con1i 121	. 2 |- (-. ((ph \/ ps) <-> ph) -> ((ph \/ ps) <-> ps))
7	6	orri 365	1 |- (((ph \/ ps) <-> ph) \/ ((ph \/ ps) <-> ps))

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

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

This theorem is referenced by: (None)