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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  7799  omwordri  7805  omass  7813  oewordri  7825  umgrclwwlkge2  27140  upgr4cycl4dv4e  27364  elspansn5  28770  atcvat3i  29592  mdsymlem5  29603  sumdmdlem  29614  cvrat4  35247  sprsymrelfolem2  42267
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