Theorem pm5.63 346

Description: Theorem *5.63 of [WhiteheadRussell] p. 125.

Assertion

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

Proof of Theorem pm5.63

Step	Hyp	Ref	Expression
1		pm2.53 254	. . . 4 |- ((ph \/ ps) -> (-. ph -> ps))
2	1	ancld 298	. . 3 |- ((ph \/ ps) -> (-. ph -> (-. ph /\ ps)))
3	2	orrd 233	. 2 |- ((ph \/ ps) -> (ph \/ (-. ph /\ ps)))
4		pm2.24 79	. . . 4 |- (ph -> (-. ph -> ps))
5		pm3.4 331	. . . 4 |- ((-. ph /\ ps) -> (-. ph -> ps))
6	4, 5	jaoi 341	. . 3 |- ((ph \/ (-. ph /\ ps)) -> (-. ph -> ps))
7	6	orrd 233	. 2 |- ((ph \/ (-. ph /\ ps)) -> (ph \/ ps))
8	3, 7	impbi 157	1 |- ((ph \/ ps) <-> (ph \/ (-. ph /\ ps)))

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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