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Theorem intn3an2d 1477
 Description: Introduction of a triple conjunct inside a contradiction. (Contributed by FL, 27-Dec-2007.) (Proof shortened by Andrew Salmon, 26-Jun-2011.)
Hypothesis
Ref Expression
intn3and.1 (𝜑 → ¬ 𝜓)
Assertion
Ref Expression
intn3an2d (𝜑 → ¬ (𝜒𝜓𝜃))

Proof of Theorem intn3an2d
StepHypRef Expression
1 intn3and.1 . 2 (𝜑 → ¬ 𝜓)
2 simp2 1134 . 2 ((𝜒𝜓𝜃) → 𝜓)
31, 2nsyl 142 1 (𝜑 → ¬ (𝜒𝜓𝜃))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ w3a 1084 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 210  df-an 400  df-3an 1086 This theorem is referenced by:  iooelexlt  34661  lenelioc  41966  icccncfext  42322  fourierdlem10  42552  fourierdlem104  42645  cznnring  44374
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