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Theorem 3ianorr 1203
Description: Triple disjunction implies negated triple conjunction. (Contributed by Jim Kingdon, 23-Dec-2018.)
Assertion
Ref Expression
3ianorr ((¬ φ ¬ ψ ¬ χ) → ¬ (φ ψ χ))

Proof of Theorem 3ianorr
StepHypRef Expression
1 simp1 903 . . 3 ((φ ψ χ) → φ)
21con3i 561 . 2 φ → ¬ (φ ψ χ))
3 simp2 904 . . 3 ((φ ψ χ) → ψ)
43con3i 561 . 2 ψ → ¬ (φ ψ χ))
5 simp3 905 . . 3 ((φ ψ χ) → χ)
65con3i 561 . 2 χ → ¬ (φ ψ χ))
72, 4, 63jaoi 1197 1 ((¬ φ ¬ ψ ¬ χ) → ¬ (φ ψ χ))
Colors of variables: wff set class
Syntax hints:  ¬ wn 3  wi 4   w3o 883   w3a 884
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 629
This theorem depends on definitions:  df-bi 110  df-3or 885  df-3an 886
This theorem is referenced by:  funtpg  4893
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