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Theorem 3impdi 1351
Description: Importation inference (undistribute conjunction). (Contributed by NM, 14-Aug-1995.)
Hypothesis
Ref Expression
3impdi.1 (((𝜑𝜓) ∧ (𝜑𝜒)) → 𝜃)
Assertion
Ref Expression
3impdi ((𝜑𝜓𝜒) → 𝜃)

Proof of Theorem 3impdi
StepHypRef Expression
1 3impdi.1 . . 3 (((𝜑𝜓) ∧ (𝜑𝜒)) → 𝜃)
21anandis 677 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323impb 1116 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 397  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  oacan  8544  omcan  8565  ecovdi  8815  distrpi  10889  axltadd  11283  ccatlcan  14664  absmulgcd  16487  axlowdimlem14  28193  fh1  30849  fh2  30850  cm2j  30851  hoadddi  31034  hosubdi  31039  leopmul2i  31366  dvconstbi  43026  eel2131  43408  uun2131  43485  uun2131p1  43486  io1ii  47455  reccot  47705  rectan  47706
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