Theorem pm5.71 748

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 252	. . . 4 |- (-. ps -> ((ph \/ ps) -> ph))
2		orc 269	. . . 4 |- (ph -> (ph \/ ps))
3	1, 2	impbid1 517	. . 3 |- (-. ps -> ((ph \/ ps) <-> ph))
4	3	anbi1d 617	. 2 |- (-. ps -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))
5		pm2.21 76	. . 3 |- (-. ch -> (ch -> ((ph \/ ps) <-> ph)))
6	5	pm5.32rd 648	. 2 |- (-. ch -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))
7	4, 6	ja 137	1 |- ((ps -> -. ch) -> (((ph \/ ps) /\ ch) <-> (ph /\ ch)))

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   \/ wo 222   /\ wa 223

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

This theorem depends on definitions:  df-bi 147  df-or 224  df-an 225

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