Theorem 3pm3.2ni 1490

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	⊢ ¬ (𝜑 ∨ 𝜓 ∨ 𝜒)

Proof of Theorem 3pm3.2ni

Step	Hyp	Ref	Expression
1		3pm3.2ni.1	. . . 4 ⊢ ¬ 𝜑
2		3pm3.2ni.2	. . . 4 ⊢ ¬ 𝜓
3	1, 2	pm3.2ni 881	. . 3 ⊢ ¬ (𝜑 ∨ 𝜓)
4		3pm3.2ni.3	. . 3 ⊢ ¬ 𝜒
5	3, 4	pm3.2ni 881	. 2 ⊢ ¬ ((𝜑 ∨ 𝜓) ∨ 𝜒)
6		df-3or 1088	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
7	5, 6	mtbir 323	1 ⊢ ¬ (𝜑 ∨ 𝜓 ∨ 𝜒)

Syntax hints:  ¬ wn 3   ∨ wo 848   ∨ w3o 1086

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 207  df-or 849  df-3or 1088

This theorem is referenced by:  poxp3  8175  cnfldfun  21378  sltsolem1  27720  usgrexmpl2nb1  47991  usgrexmpl2nb2  47992  usgrexmpl2nb4  47994  usgrexmpl2nb5  47995