Theorem pm4.83 895

Description: Theorem *4.83 of [WhiteheadRussell] p. 122. (Contributed by NM, 3-Jan-2005.)

Assertion

Ref	Expression
pm4.83	|- (((ph -> ps) /\ (-. ph -> ps)) <-> ps)

Proof of Theorem pm4.83

Step	Hyp	Ref	Expression
1		exmid 404	. . 3 |- (ph \/ -. ph)
2	1	a1bi 327	. 2 |- (ps <-> ((ph \/ -. ph) -> ps))
3		jaob 758	. 2 |- (((ph \/ -. ph) -> ps) <-> ((ph -> ps) /\ (-. ph -> ps)))
4	2, 3	bitr2i 241	1 |- (((ph -> ps) /\ (-. ph -> ps)) <-> ps)

Syntax hints:  -. wn 3   -> wi 4   <-> 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: (None)