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Theorem intn3an3d 1436
 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 1056 . 2 ((𝜒𝜃𝜓) → 𝜓)
31, 2nsyl 134 1 (𝜑 → ¬ (𝜒𝜃𝜓))
 Colors of variables: wff setvar class Syntax hints:  ¬ wn 3   → wi 4   ∧ w3a 1031 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  df-3an 1033 This theorem is referenced by:  en3lp  8396  winainflem  9394  ccatalpha  13228  spthispth  26103  2spotdisj  26588  gtnelioc  38559  icccncfext  38773  fourierdlem10  39010  clwwlks  41187
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