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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 851 | . 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜑) |
6 | 1, 5 | mto 198 | 1 ⊢ ¬ (𝜑 ∨ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 841 |
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 208 df-or 842 |
This theorem is referenced by: snsn0non 6303 canthp1lem2 10064 recgt0ii 11535 xrltnr 12504 pnfnlt 12513 nltmnf 12514 lhop 24542 2lgslem4 25910 axlowdimlem13 26668 3pm3.2ni 32841 nosgnn0 33063 clsk1indlem4 40274 clsk1indlem1 40275 dandysum2p2e4 43115 smndex1n0mnd 43982 |
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