MPE Home Metamath Proof Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  MPE Home  >  Th. List  >  3impdir Structured version   Visualization version   GIF version

Theorem 3impdir 1444
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 658 . 2 (((𝜑𝜒) ∧ 𝜓) → 𝜃)
323impa 1100 1 ((𝜑𝜒𝜓) → 𝜃)
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 382  w3a 1071
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 197  df-an 383  df-3an 1073
This theorem is referenced by:  divcan7  10936  ccatrcan  13678  his7  28283  his2sub2  28286  hoadddir  28999  nndivsub  32789  rdgeqoa  33551  eel3132  39462  3impdirp1  39565
  Copyright terms: Public domain W3C validator