Theorem pm5.63 890

Description: Theorem *5.63 of [WhiteheadRussell] p. 125. (Contributed by NM, 3-Jan-2005.) (Proof shortened by Wolf Lammen, 25-Dec-2012.)

Assertion

Ref	Expression
pm5.63	|- ((ph \/ ps) <-> (ph \/ (-. ph /\ ps)))

Proof of Theorem pm5.63

Step	Hyp	Ref	Expression
1		exmid 404	. . 3 |- (ph \/ -. ph)
2		ordi 834	. . 3 |- ((ph \/ (-. ph /\ ps)) <-> ((ph \/ -. ph) /\ (ph \/ ps)))
3	1, 2	mpbiran 884	. 2 |- ((ph \/ (-. ph /\ ps)) <-> (ph \/ ps))
4	3	bicomi 193	1 |- ((ph \/ ps) <-> (ph \/ (-. ph /\ ps)))

Syntax hints:  -. wn 3   <-> 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:  cad1  1398