Theorem pm2.01d 172

Description: Deduction based on reductio ad absurdum. (Contributed by NM, 18-Aug-1993.) (Proof shortened by Wolf Lammen, 5-Mar-2013.)

Hypothesis

Ref	Expression
pm2.01d.1	|- ( ph -> ( ps -> -. ps ) )

Assertion

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

Proof of Theorem pm2.01d

Step	Hyp	Ref	Expression
1		pm2.01d.1	. 2 |- ( ph -> ( ps -> -. ps ) )
2		id 22	. 2 |- ( -. ps -> -. ps )
3	1, 2	pm2.61d1 162	1 |- ( ph -> -. ps )

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:  pm2.65d  178  pm2.01da  443  swopo  4727  oalimcl  7216  rankcf  9153  prlem934  9409  supsrlem  9486  rpnnen1lem5  11245  rennim  13246  smu01lem  14402  opsrtoslem2  18651  cfinufil  20885  alexsub  21002  ostth3  24418  4cyclusnfrgra  25689  cvnref  27886  pconcon  29906  untelirr  30287  dfon2lem4  30383  amosym1  31035  heiborlem10  32059  lindslinindsimp1  39843