Theorem pm4.43 431

Description: Theorem *4.43 of [WhiteheadRussell] p. 119.

Assertion

Ref	Expression
pm4.43	|- (ph <-> ((ph \/ ps) /\ (ph \/ -. ps)))

Proof of Theorem pm4.43

Step	Hyp	Ref	Expression
1		orc 269	. . 3 |- (ph -> (ph \/ ps))
2		orc 269	. . 3 |- (ph -> (ph \/ -. ps))
3	1, 2	jca 288	. 2 |- (ph -> ((ph \/ ps) /\ (ph \/ -. ps)))
4		pm2.64 429	. . 3 |- ((ph \/ ps) -> ((ph \/ -. ps) -> ph))
5	4	imp 350	. 2 |- (((ph \/ ps) /\ (ph \/ -. ps)) -> ph)
6	3, 5	impbi 157	1 |- (ph <-> ((ph \/ ps) /\ (ph \/ -. ps)))

Syntax hints:  -. wn 2   <-> 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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