Theorem pm5.24 672

Description: Theorem *5.24 of [WhiteheadRussell] p. 124.

Assertion

Ref	Expression
pm5.24	|- (-. ((ph /\ ps) \/ (-. ph /\ -. ps)) <-> ((ph /\ -. ps) \/ (ps /\ -. ph)))

Proof of Theorem pm5.24

Step	Hyp	Ref	Expression
1		dfbi3 670	. . 3 |- ((ph <-> ps) <-> ((ph /\ ps) \/ (-. ph /\ -. ps)))
2	1	negbii 187	. 2 |- (-. (ph <-> ps) <-> -. ((ph /\ ps) \/ (-. ph /\ -. ps)))
3		xor 671	. 2 |- (-. (ph <-> ps) <-> ((ph /\ -. ps) \/ (ps /\ -. ph)))
4	2, 3	bitr3 175	1 |- (-. ((ph /\ ps) \/ (-. ph /\ -. ps)) <-> ((ph /\ -. ps) \/ (ps /\ -. ph)))

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

This theorem is referenced by:  xor2 673

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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