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Theorem intn3an3d 1482
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 1139 . 2 ((𝜒𝜃𝜓) → 𝜓)
31, 2nsyl 140 1 (𝜑 → ¬ (𝜒𝜃𝜓))
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wi 4  w3a 1088
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 206  df-an 398  df-3an 1090
This theorem is referenced by:  frxp2  8130  frxp3  8137  en3lp  9609  winainflem  10688  ccatalpha  14543  clwwlk  29236  nlimsuc  42192  gtnelioc  44204  icccncfext  44603  fourierdlem10  44833
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