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Theorem 3ianorr 1241
Description: Triple disjunction implies negated triple conjunction. (Contributed by Jim Kingdon, 23-Dec-2018.)
Assertion
Ref Expression
3ianorr ((¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒) → ¬ (𝜑𝜓𝜒))

Proof of Theorem 3ianorr
StepHypRef Expression
1 simp1 939 . . 3 ((𝜑𝜓𝜒) → 𝜑)
21con3i 595 . 2 𝜑 → ¬ (𝜑𝜓𝜒))
3 simp2 940 . . 3 ((𝜑𝜓𝜒) → 𝜓)
43con3i 595 . 2 𝜓 → ¬ (𝜑𝜓𝜒))
5 simp3 941 . . 3 ((𝜑𝜓𝜒) → 𝜒)
65con3i 595 . 2 𝜒 → ¬ (𝜑𝜓𝜒))
72, 4, 63jaoi 1235 1 ((¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒) → ¬ (𝜑𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  w3o 919  w3a 920
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663
This theorem depends on definitions:  df-bi 115  df-3or 921  df-3an 922
This theorem is referenced by:  funtpg  5016
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