Theorem pm2.01 180

Description: Reductio ad absurdum. Theorem *2.01 of [WhiteheadRussell] p. 100. Also called the weak Clavius law, and provable in minimal calculus, contrary to the Clavius law pm2.18 122. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Mel L. O'Cat, 21-Nov-2008.) (Proof shortened by Wolf Lammen, 31-Oct-2012.)

Assertion

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

Proof of Theorem pm2.01

Step	Hyp	Ref	Expression
1		id 22	. 2 |- ( -. ph -> -. ph )
2	1, 1	ja 173	1 |- ( ( ph -> -. ph ) -> -. ph )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is referenced by:  bijust  195  pm4.8  380  axin1  2590  dtrucor2  4901  ominf  8172  elirr  8505  hfninf  32293  bj-pm2.01i  32550  bj-nimn  32551  bj-dtrucor2v  32801