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Theorem intn3an1d 1470
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
intn3an1d (𝜑 → ¬ (𝜓𝜒𝜃))

Proof of Theorem intn3an1d
StepHypRef Expression
1 intn3and.1 . 2 (𝜑 → ¬ 𝜓)
2 simp1 1128 . 2 ((𝜓𝜒𝜃) → 𝜓)
31, 2nsyl 142 1 (𝜑 → ¬ (𝜓𝜒𝜃))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  w3a 1079
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 208  df-an 397  df-3an 1081
This theorem is referenced by: (None)
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