Theorem pm2.01 88

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 84	. . 3 |- (-. -. ph -> ph)
2	1	imim1i 16	. 2 |- ((ph -> -. ph) -> (-. -. ph -> -. ph))
3		pm2.18 81	. 2 |- ((-. -. ph -> -. ph) -> -. ph)
4	2, 3	syl 10	1 |- ((ph -> -. ph) -> -. ph)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  pm2.01d 89  bijust 145  pm4.8 162  dtrucor2 2770  ominf 4517  elirr 4582  ruclem39 7508

This theorem was proved from axioms:  ax-1 4  ax-2 5  ax-3 6  ax-mp 7

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