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Theorem mpanl2 700
 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 𝜓
mpanl2.2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
Assertion
Ref Expression
mpanl2 ((𝜑𝜒) → 𝜃)

Proof of Theorem mpanl2
StepHypRef Expression
1 mpanl2.1 . . 3 𝜓
21jctr 528 . 2 (𝜑 → (𝜑𝜓))
3 mpanl2.2 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
42, 3sylan 583 1 ((𝜑𝜒) → 𝜃)
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 399 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 210  df-an 400 This theorem is referenced by:  mpanr1  702  mp3an2  1446  reuss  4239  tfrlem11  8025  tfr3  8036  oe0  8148  dif1en  8753  indpi  10336  map2psrpr  10539  axcnre  10593  muleqadd  11291  divdiv2  11359  addltmul  11879  supxrpnf  12719  supxrunb1  12720  supxrunb2  12721  iimulcl  23583  clwwlknonex2lem2  27937  nmopadjlem  29916  nmopcoadji  29928  opsqrlem6  29972  hstrbi  30093  sgncl  31972  poimirlem3  35211  aacllem  45495
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