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Theorem mpanl2 684
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 516 . 2 (𝜑 → (𝜑𝜓))
3 mpanl2.2 . 2 (((𝜑𝜓) ∧ 𝜒) → 𝜃)
42, 3sylan 571 1 ((𝜑𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 198  df-an 385
This theorem is referenced by:  mpanr1  686  mp3an2  1566  reuss  4120  tfrlem11  7727  tfr3  7738  oe0  7846  dif1en  8439  indpi  10021  map2psrpr  10223  axcnre  10277  muleqadd  10963  divdiv2  11029  addltmul  11542  frnnn0supp  11622  supxrpnf  12373  supxrunb1  12374  supxrunb2  12375  iimulcl  22957  clwwlknonex2lem2  27287  nmopadjlem  29286  nmopcoadji  29298  opsqrlem6  29342  hstrbi  29463  sgncl  30935  poimirlem3  33731  aacllem  43123
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