Theorem pm2.01 103

Description: Reductio ad absurdum. Theorem *2.01 of [WhiteheadRussell] p. 100. (The proof was shortened by O'Cat, 21-Nov-2008.

Assertion

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

Proof of Theorem pm2.01

Step	Hyp	Ref	Expression
1		pm2.18 96	. 2 |- ((-. ph -> ph) -> ph)
2		looinv 98	. 2 |- (((-. ph -> ph) -> ph) -> ((ph -> -. ph) -> -. ph))
3	1, 2	ax-mp 7	1 |- ((ph -> -. ph) -> -. ph)

Syntax hints:  -. wn 2   -> wi 3

This theorem is referenced by:  pm2.01d 104  bijust 161  pm4.8 178  dtrucor2 3334  ominf 5432  elirr 5511  elirrOLD 5512  ruclem39 8612  usinuniop 10133

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

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