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  4621  funun  5361  pwuninel2  6426  swoer  6706  swoord1  6707  swoord2  6708  ssfirab  7094  djune  7241  exmidaclem  7386  sucpw1nss3  7416  onntri35  7418  onntri45  7422  elnnz  9452  lbioog  10105  ubioog  10106  fzneuz  10293  fzodisj  10372  fzodisjsn  10376  infssuzex  10448  fxnn0nninf  10656  zfz1isolemiso  11056  swrd0g  11187  infpnlem1  12877  exmidunben  12992  lgsdir2lem2  15702  2lgslem3  15774