Theorem pm4.82 739

Description: Theorem *4.82 of [WhiteheadRussell] p. 122.

Assertion

Ref	Expression
pm4.82	|- (((ph -> ps) /\ (ph -> -. ps)) <-> -. ph)

Proof of Theorem pm4.82

Step	Hyp	Ref	Expression
1		pm2.65 134	. . 3 |- ((ph -> ps) -> ((ph -> -. ps) -> -. ph))
2	1	imp 350	. 2 |- (((ph -> ps) /\ (ph -> -. ps)) -> -. ph)
3		pm2.21 76	. . 3 |- (-. ph -> (ph -> ps))
4		pm2.21 76	. . 3 |- (-. ph -> (ph -> -. ps))
5	3, 4	jca 288	. 2 |- (-. ph -> ((ph -> ps) /\ (ph -> -. ps)))
6	2, 5	impbi 157	1 |- (((ph -> ps) /\ (ph -> -. ps)) <-> -. ph)

Syntax hints:  -. wn 2   -> wi 3   <-> wb 146   /\ 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-an 225

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