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Theorem 3ianorr 1309
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 997 . . 3 ((𝜑𝜓𝜒) → 𝜑)
21con3i 632 . 2 𝜑 → ¬ (𝜑𝜓𝜒))
3 simp2 998 . . 3 ((𝜑𝜓𝜒) → 𝜓)
43con3i 632 . 2 𝜓 → ¬ (𝜑𝜓𝜒))
5 simp3 999 . . 3 ((𝜑𝜓𝜒) → 𝜒)
65con3i 632 . 2 𝜒 → ¬ (𝜑𝜓𝜒))
72, 4, 63jaoi 1303 1 ((¬ 𝜑 ∨ ¬ 𝜓 ∨ ¬ 𝜒) → ¬ (𝜑𝜓𝜒))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4  w3o 977  w3a 978
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 614  ax-in2 615  ax-io 709
This theorem depends on definitions:  df-bi 117  df-3or 979  df-3an 980
This theorem is referenced by:  funtpg  5267
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