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  6434  swoer  6716  swoord1  6717  swoord2  6718  ssfirab  7109  djune  7256  exmidaclem  7401  sucpw1nss3  7431  onntri35  7433  onntri45  7437  elnnz  9467  lbioog  10121  ubioog  10122  fzneuz  10309  fzodisj  10388  fzodisjsn  10392  infssuzex  10465  fxnn0nninf  10673  zfz1isolemiso  11074  swrd0g  11208  infpnlem1  12898  exmidunben  13013  lgsdir2lem2  15724  2lgslem3  15796