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Mirrors > Home > MPE Home > Th. List > pm3.2ni | Structured version Visualization version GIF version |
Description: Infer negated disjunction of negated premises. (Contributed by NM, 4-Apr-1995.) |
Ref | Expression |
---|---|
pm3.2ni.1 | ⊢ ¬ 𝜑 |
pm3.2ni.2 | ⊢ ¬ 𝜓 |
Ref | Expression |
---|---|
pm3.2ni | ⊢ ¬ (𝜑 ∨ 𝜓) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | pm3.2ni.1 | . 2 ⊢ ¬ 𝜑 | |
2 | id 22 | . . 3 ⊢ (𝜑 → 𝜑) | |
3 | pm3.2ni.2 | . . . 4 ⊢ ¬ 𝜓 | |
4 | 3 | pm2.21i 119 | . . 3 ⊢ (𝜓 → 𝜑) |
5 | 2, 4 | jaoi 855 | . 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜑) |
6 | 1, 5 | mto 196 | 1 ⊢ ¬ (𝜑 ∨ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 845 |
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 206 df-or 846 |
This theorem is referenced by: 3pm3.2ni 1488 snsn0non 6489 canthp1lem2 10650 recgt0ii 12122 xrltnr 13101 pnfnlt 13110 nltmnf 13111 smndex1n0mnd 18795 lhop 25540 2lgslem4 26916 nosgnn0 27168 axlowdimlem13 28250 clsk1indlem4 42877 clsk1indlem1 42878 dandysum2p2e4 45787 |
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