Theorem pm5.15 665

Description: Theorem *5.15 of [WhiteheadRussell] p. 124.

Assertion

Ref	Expression
pm5.15	|- ((ph <-> ps) \/ (ph <-> -. ps))

Proof of Theorem pm5.15

Step	Hyp	Ref	Expression
1		pm5.18 659	. . . 4 |- ((ph <-> ps) <-> -. (ph <-> -. ps))
2	1	biimpr 152	. . 3 |- (-. (ph <-> -. ps) -> (ph <-> ps))
3	2	con1i 96	. 2 |- (-. (ph <-> ps) -> (ph <-> -. ps))
4	3	orri 231	1 |- ((ph <-> ps) \/ (ph <-> -. ps))

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

This theorem is referenced by:  sbc2or 1955

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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