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Theorem 3impdi 1304
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 592 . 2 ((𝜑 ∧ (𝜓𝜒)) → 𝜃)
323impb 1201 1 ((𝜑𝜓𝜒) → 𝜃)
Colors of variables: wff set class
Syntax hints:  wi 4  wa 104  w3a 980
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108
This theorem depends on definitions:  df-bi 117  df-3an 982
This theorem is referenced by:  ecovdi  6700  ecovidi  6701  distrpig  7393  mulcanenq  7445  mulcanenq0ec  7505  distrnq0  7519  axltadd  8089  absmulgcd  12154
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