Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
||
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 857 | . 2 ⊢ ((𝜑 ∨ 𝜓) → 𝜑) |
6 | 1, 5 | mto 200 | 1 ⊢ ¬ (𝜑 ∨ 𝜓) |
Colors of variables: wff setvar class |
Syntax hints: ¬ wn 3 ∨ wo 847 |
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 848 |
This theorem is referenced by: snsn0non 6337 canthp1lem2 10272 recgt0ii 11743 xrltnr 12716 pnfnlt 12725 nltmnf 12726 smndex1n0mnd 18344 lhop 24918 2lgslem4 26292 axlowdimlem13 27050 3pm3.2ni 33376 nosgnn0 33603 clsk1indlem4 41339 clsk1indlem1 41340 dandysum2p2e4 44173 |
Copyright terms: Public domain | W3C validator |