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Theorem 3pm3.2ni 33000
Description: Triple negated disjunction introduction. (Contributed by Scott Fenton, 20-Apr-2011.)
Hypotheses
Ref Expression
3pm3.2ni.1 ¬ 𝜑
3pm3.2ni.2 ¬ 𝜓
3pm3.2ni.3 ¬ 𝜒
Assertion
Ref Expression
3pm3.2ni ¬ (𝜑𝜓𝜒)

Proof of Theorem 3pm3.2ni
StepHypRef Expression
1 3pm3.2ni.1 . . . 4 ¬ 𝜑
2 3pm3.2ni.2 . . . 4 ¬ 𝜓
31, 2pm3.2ni 878 . . 3 ¬ (𝜑𝜓)
4 3pm3.2ni.3 . . 3 ¬ 𝜒
53, 4pm3.2ni 878 . 2 ¬ ((𝜑𝜓) ∨ 𝜒)
6 df-3or 1085 . 2 ((𝜑𝜓𝜒) ↔ ((𝜑𝜓) ∨ 𝜒))
75, 6mtbir 326 1 ¬ (𝜑𝜓𝜒)
Colors of variables: wff setvar class
Syntax hints:  ¬ wn 3  wo 844  w3o 1083
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 210  df-or 845  df-3or 1085
This theorem is referenced by:  sltsolem1  33237
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