Theorem pm5.71 902

Description: Theorem *5.71 of [WhiteheadRussell] p. 125. (Contributed by Roy F. Longton, 23-Jun-2005.)

Assertion

Ref	Expression
pm5.71	|- ((ps -> -. ch) -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))

Proof of Theorem pm5.71

Step	Hyp	Ref	Expression
1		orel2 372	. . . 4 |- (-. ps -> ((ph \/ ps) -> ph))
2		orc 374	. . . 4 |- (ph -> (ph \/ ps))
3	1, 2	impbid1 194	. . 3 |- (-. ps -> ((ph \/ ps) <-> ph))
4	3	anbi1d 685	. 2 |- (-. ps -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))
5		pm2.21 100	. . 3 |- (-. ch -> (ch -> ((ph \/ ps) <-> ph)))
6	5	pm5.32rd 621	. 2 |- (-. ch -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))
7	4, 6	ja 153	1 |- ((ps -> -. ch) -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))

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)