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Theorem mpanl2 426
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 308 . 2  |-  ( ph  ->  ( ph  /\  ps ) )
3 mpanl2.2 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
42, 3sylan 277 1  |-  ( (
ph  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 102
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106
This theorem is referenced by:  mpanr1  428  mp3an2  1261  reuss  3280  tfri3  6132  prarloclemarch2  6978  prarloclemlt  7052  prsradd  7331  pitonnlem2  7384  axcnre  7416  muleqadd  8137  divdivap2  8191  addltmul  8652
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