Theorem pm4.42 765

Description: Theorem *4.42 of [WhiteheadRussell] p. 119. (Contributed by Roy F. Longton, 21-Jun-2005.)

Assertion

Ref	Expression
pm4.42	|- (ph <-> ((ph /\ ps) \/ (ph /\ -. ps)))

Proof of Theorem pm4.42

Step	Hyp	Ref	Expression
1		dedlema 759	. 2 |- (ps -> (ph <-> ((ph /\ ps) \/ (ph /\ -. ps))))
2		dedlemb 760	. 2 |- (-. ps -> (ph <-> ((ph /\ ps) \/ (ph /\ -. ps))))
3	1, 2	pm2.61i 126	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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