Theorem pm4.44 345

Description: Theorem *4.44 of [WhiteheadRussell] p. 119.

Assertion

Ref	Expression
pm4.44	|- (ph <-> (ph \/ (ph /\ ps)))

Proof of Theorem pm4.44

Step	Hyp	Ref	Expression
1		orc 269	. 2 |- (ph -> (ph \/ (ph /\ ps)))
2		id 59	. . 3 |- (ph -> ph)
3		pm3.26 319	. . 3 |- ((ph /\ ps) -> ph)
4	2, 3	jaoi 341	. 2 |- ((ph \/ (ph /\ ps)) -> ph)
5	1, 4	impbi 157	1 |- (ph <-> (ph \/ (ph /\ ps)))

Syntax hints:   <-> 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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