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Theorem imp4c 410
 Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
imp4c (𝜑 → (((𝜓𝜒) ∧ 𝜃) → 𝜏))

Proof of Theorem imp4c
StepHypRef Expression
1 imp4.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21impd 396 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32impd 396 1 (𝜑 → (((𝜓𝜒) ∧ 𝜃) → 𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 382 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 This theorem is referenced by:  imp44  415  imp5g  428  omordi  7800  omwordri  7806  omass  7814  oewordri  7826  umgrclwwlkge2  27141  upgr4cycl4dv4e  27365  elspansn5  28773  atcvat3i  29595  mdsymlem5  29606  sumdmdlem  29617  cvrat4  35251  sprsymrelfolem2  42271
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