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Theorem imp4c 615
 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 446 . 2 (𝜑 → ((𝜓𝜒) → (𝜃𝜏)))
32impd 446 1 (𝜑 → (((𝜓𝜒) ∧ 𝜃) → 𝜏))
 Colors of variables: wff setvar class Syntax hints:   → wi 4   ∧ wa 383 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 196  df-an 385 This theorem is referenced by:  imp44  620  imp5g  624  omordi  7533  omwordri  7539  omass  7547  oewordri  7559  elspansn5  27817  atcvat3i  28639  mdsymlem5  28650  sumdmdlem  28661  cvrat4  33747  umgrclwwlksge2  41219  upgr4cycl4dv4e  41352
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