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Theorem 3impdi 1347
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 675 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323impb 1112 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 395  w3a 1084
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 396  df-3an 1086
This theorem is referenced by:  oacan  8543  omcan  8564  ecovdi  8815  distrpi  10889  axltadd  11284  ccatlcan  14665  absmulgcd  16488  axlowdimlem14  28682  fh1  31340  fh2  31341  cm2j  31342  hoadddi  31525  hosubdi  31530  leopmul2i  31857  dvconstbi  43582  eel2131  43964  uun2131  44041  uun2131p1  44042  io1ii  47741  reccot  47991  rectan  47992
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