Theorem pm5.16 667

Description: Theorem *5.16 of [WhiteheadRussell] p. 124.

Assertion

Ref	Expression
pm5.16	|- -. ((ph <-> ps) /\ (ph <-> -. ps))

Proof of Theorem pm5.16

Step	Hyp	Ref	Expression
1		pm5.18 660	. . . 4 |- ((ph <-> ps) <-> -. (ph <-> -. ps))
2	1	biimp 151	. . 3 |- ((ph <-> ps) -> -. (ph <-> -. ps))
3		pm4.62 235	. . 3 |- (((ph <-> ps) -> -. (ph <-> -. ps)) <-> (-. (ph <-> ps) \/ -. (ph <-> -. ps)))
4	2, 3	mpbi 189	. 2 |- (-. (ph <-> ps) \/ -. (ph <-> -. ps))
5		ianor 305	. 2 |- (-. ((ph <-> ps) /\ (ph <-> -. ps)) <-> (-. (ph <-> ps) \/ -. (ph <-> -. ps)))
6	4, 5	mpbir 190	1 |- -. ((ph <-> ps) /\ (ph <-> -. ps))

Syntax hints:  -. wn 2   -> wi 3   <-> 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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