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Theorem mpanl2 681
Description: An inference based on modus ponens. (Contributed by NM, 16-Aug-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypotheses
Ref Expression
mpanl2.1  |-  ps
mpanl2.2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
Assertion
Ref Expression
mpanl2  |-  ( (
ph  /\  ch )  ->  th )

Proof of Theorem mpanl2
StepHypRef Expression
1 mpanl2.1 . . 3  |-  ps
21jctr 542 . 2  |-  ( ph  ->  ( ph  /\  ps ) )
3 mpanl2.2 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
42, 3sylan 471 1  |-  ( (
ph  /\  ch )  ->  th )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8
This theorem depends on definitions:  df-bi 185  df-an 371
This theorem is referenced by:  mpanr1  683  mp3an2  1302  reuss  3631  tfrlem11  6847  tfr3  6858  oe0  6962  dif1enOLD  7544  dif1en  7545  noinfepOLD  7866  indpi  9076  map2psrpr  9277  axcnre  9331  muleqadd  9980  divdiv2  10043  addltmul  10560  frnnn0supp  10633  supxrpnf  11281  supxrunb1  11282  supxrunb2  11283  iimulcl  20509  eigposi  25240  nmopadjlem  25493  nmopcoadji  25505  opsqrlem6  25549  hstrbi  25670  numclwwlkovf2ex  30679
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