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Theorem mpanr1 434
Description: An inference based on modus ponens. (Contributed by NM, 3-May-1994.) (Proof shortened by Andrew Salmon, 7-May-2011.)
Hypotheses
Ref Expression
mpanr1.1  |-  ps
mpanr1.2  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
Assertion
Ref Expression
mpanr1  |-  ( (
ph  /\  ch )  ->  th )

Proof of Theorem mpanr1
StepHypRef Expression
1 mpanr1.1 . 2  |-  ps
2 mpanr1.2 . . 3  |-  ( (
ph  /\  ( ps  /\ 
ch ) )  ->  th )
32anassrs 398 . 2  |-  ( ( ( ph  /\  ps )  /\  ch )  ->  th )
41, 3mpanl2 432 1  |-  ( (
ph  /\  ch )  ->  th )
Colors of variables: wff set class
Syntax hints:    -> wi 4    /\ wa 103
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107
This theorem is referenced by:  mpanr12  436  axcnre  7712  rec11api  8536  divdiv23apzi  8548  recp1lt1  8680  divgt0i  8691  divge0i  8692  ltreci  8693  lereci  8694  lt2msqi  8695  le2msqi  8696  msq11i  8697  ltdiv23i  8707  ge0gtmnf  9635  sqrt11i  10935  sqrtmuli  10936  sqrtmsq2i  10938  sqrtlei  10939  sqrtlti  10940  cos01gt0  11503
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