Theorem nsyl 631

Description: A negated syllogism inference. (Contributed by NM, 31-Dec-1993.) (Proof shortened by Wolf Lammen, 2-Mar-2013.)

Hypotheses

Ref	Expression
nsyl.1	|- ( ph -> -. ps )
nsyl.2	|- ( ch -> ps )

Assertion

Ref	Expression
nsyl	|- ( ph -> -. ch )

Proof of Theorem nsyl

Step	Hyp	Ref	Expression
1		nsyl.1	. . 3 |- ( ph -> -. ps )
2		nsyl.2	. . 3 |- ( ch -> ps )
3	1, 2	nsyl3 629	. 2 |- ( ch -> -. ph )
4	3	con2i 630	1 |- ( ph -> -. ch )

Syntax hints:   -. wn 3   -> wi 4

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-in1 617  ax-in2 618

This theorem is referenced by:  con3i  635  pm4.52im  755  intnand  936  intnanrd  937  intn3an1d  1390  intn3an2d  1391  intn3an3d  1392  camestres  2183  camestros  2187  calemes  2194  calemos  2197  unssin  3443  inssun  3444  onsucelsucexmid  4622  funun  5362  pwuninel2  6428  swoer  6708  swoord1  6709  swoord2  6710  ssfirab  7098  djune  7245  exmidaclem  7390  sucpw1nss3  7420  onntri35  7422  onntri45  7426  elnnz  9456  lbioog  10109  ubioog  10110  fzneuz  10297  fzodisj  10376  fzodisjsn  10380  infssuzex  10453  fxnn0nninf  10661  zfz1isolemiso  11061  swrd0g  11192  infpnlem1  12882  exmidunben  12997  lgsdir2lem2  15708  2lgslem3  15780