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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  8548  omcan  8569  ecovdi  8819  distrpi  10893  axltadd  11287  ccatlcan  14668  absmulgcd  16491  axlowdimlem14  28213  fh1  30871  fh2  30872  cm2j  30873  hoadddi  31056  hosubdi  31061  leopmul2i  31388  dvconstbi  43093  eel2131  43475  uun2131  43552  uun2131p1  43553  io1ii  47553  reccot  47803  rectan  47804
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