Theorem 3pm3.2ni 1519

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 894	. . 3 ⊢ ¬ (𝜑 ∨ 𝜓)
4		3pm3.2ni.3	. . 3 ⊢ ¬ 𝜒
5	3, 4	pm3.2ni 894	. 2 ⊢ ¬ ((𝜑 ∨ 𝜓) ∨ 𝜒)
6		df-3or 1104	. 2 ⊢ ((𝜑 ∨ 𝜓 ∨ 𝜒) ↔ ((𝜑 ∨ 𝜓) ∨ 𝜒))
7	5, 6	mtbir 326	1 ⊢ ¬ (𝜑 ∨ 𝜓 ∨ 𝜒)

This proof depends on syntax axioms:  ¬ wn 3   ∨ wo 861   ∨ w3o 1102

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This proof depends on definitions:  df-bi 210  df-or 862  df-3or 1104

This theorem is used by:  poxp3  8160  cnfldfun  21685  ltssolem1  28025  usgrexmpl2nb1  49099  usgrexmpl2nb2  49100  usgrexmpl2nb4  49102  usgrexmpl2nb5  49103