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Theorem 3ianorr 1204
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 904 . . 3 ((𝜑𝜓𝜒) → 𝜑)
21con3i 562 . 2 𝜑 → ¬ (𝜑𝜓𝜒))
3 simp2 905 . . 3 ((𝜑𝜓𝜒) → 𝜓)
43con3i 562 . 2 𝜓 → ¬ (𝜑𝜓𝜒))
5 simp3 906 . . 3 ((𝜑𝜓𝜒) → 𝜒)
65con3i 562 . 2 𝜒 → ¬ (𝜑𝜓𝜒))
72, 4, 63jaoi 1198 1 ((¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒) → ¬ (𝜑𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  w3o 884  w3a 885
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-in1 544  ax-in2 545  ax-io 630
This theorem depends on definitions:  df-bi 110  df-3or 886  df-3an 887
This theorem is referenced by:  funtpg  4911
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