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Theorem 3impdir 1453
Description: Importation inference (undistribute conjunction). (Contributed by NM, 20-Aug-1995.)
Hypothesis
Ref Expression
3impdir.1 (((𝜑𝜓) ∧ (𝜒𝜓)) → 𝜃)
Assertion
Ref Expression
3impdir ((𝜑𝜒𝜓) → 𝜃)

Proof of Theorem 3impdir
StepHypRef Expression
1 3impdir.1 . . 3 (((𝜑𝜓) ∧ (𝜒𝜓)) → 𝜃)
21anandirs 661 . 2 (((𝜑𝜒) ∧ 𝜓) → 𝜃)
323impa 1129 1 ((𝜑𝜒𝜓) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384  w3a 1100
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  df-3an 1102
This theorem is referenced by:  divcan7  11015  ccatrcan  13693  his7  28271  his2sub2  28274  hoadddir  28987  nndivsub  32768  rdgeqoa  33529  eel3132  39432  3impdirp1  39534
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