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Theorem intn3an3d 1435
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
intn3an3d (𝜑 → ¬ (𝜒𝜃𝜓))

Proof of Theorem intn3an3d
StepHypRef Expression
1 intn3and.1 . 2 (𝜑 → ¬ 𝜓)
2 simp3 1055 . 2 ((𝜒𝜃𝜓) → 𝜓)
31, 2nsyl 133 1 (𝜑 → ¬ (𝜒𝜃𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  w3a 1030
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 195  df-an 384  df-3an 1032
This theorem is referenced by:  en3lp  8370  winainflem  9368  ccatalpha  13171  spthispth  25866  2spotdisj  26351  gtnelioc  38360  icccncfext  38574  fourierdlem10  38811  clwwlks  41186
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