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Theorem imp4d 617
Description: An importation inference. (Contributed by NM, 26-Apr-1994.)
Hypothesis
Ref Expression
imp4.1 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
Assertion
Ref Expression
imp4d (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))

Proof of Theorem imp4d
StepHypRef Expression
1 imp4.1 . . 3 (𝜑 → (𝜓 → (𝜒 → (𝜃𝜏))))
21imp4a 613 . 2 (𝜑 → (𝜓 → ((𝜒𝜃) → 𝜏)))
32impd 447 1 (𝜑 → ((𝜓 ∧ (𝜒𝜃)) → 𝜏))
Colors of variables: wff setvar class
Syntax hints:  wi 4  wa 384
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 386
This theorem is referenced by:  imp45  622  tfrlem9  7429  uzind  11416  facdiv  13017  cvrexchlem  34206
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