Theorem pm2.01 80

Description: Reductio ad absurdum. Theorem *2.01 of [WhiteheadRussell] p. 100.

Assertion

Ref	Expression
pm2.01	|- ((ph -> -. ph) -> -. ph)

Proof of Theorem pm2.01

Step	Hyp	Ref	Expression
1		nega 78	. . 3 |- (-. -. ph -> ph)
2	1	syl4 19	. 2 |- ((ph -> -. ph) -> (-. -. ph -> -. ph))
3		pm2.18 75	. 2 |- ((-. -. ph -> -. ph) -> -. ph)
4	2, 3	syl 12	1 |- ((ph -> -. ph) -> -. ph)

Syntax hints:  -. wn 1   -> wi 2

This theorem is referenced by:  pm2.01d 81  pm2.65i 116  bijust 126  ominf 3423  eirr 3450  ruclem39 4923

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

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