Theorem pm5.61 447

Description: Theorem *5.61 of [WhiteheadRussell] p. 125.

Assertion

Ref	Expression
pm5.61	|- (((ph \/ ps) /\ -. ps) <-> (ph /\ -. ps))

Proof of Theorem pm5.61

Step	Hyp	Ref	Expression
1		orel2 252	. . 3 |- (-. ps -> ((ph \/ ps) -> ph))
2	1	imdistanri 444	. 2 |- (((ph \/ ps) /\ -. ps) -> (ph /\ -. ps))
3		orc 269	. . 3 |- (ph -> (ph \/ ps))
4	3	anim1i 334	. 2 |- ((ph /\ -. ps) -> ((ph \/ ps) /\ -. ps))
5	2, 4	impbi 157	1 |- (((ph \/ ps) /\ -. ps) <-> (ph /\ -. ps))

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

This theorem is referenced by:  oranabs 580  difprsn 2456  uninqs 10342

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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