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Mirrors > Home > ILE Home > Th. List > pm3.2ni | 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 19 | . . 3 ⊢ (φ → φ) | |
3 | pm3.2ni.2 | . . . 4 ⊢ ¬ ψ | |
4 | 3 | pm2.21i 574 | . . 3 ⊢ (ψ → φ) |
5 | 2, 4 | jaoi 635 | . 2 ⊢ ((φ ∨ ψ) → φ) |
6 | 1, 5 | mto 587 | 1 ⊢ ¬ (φ ∨ ψ) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∨ wo 628 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 |
This theorem depends on definitions: df-bi 110 |
This theorem is referenced by: xrltnr 8471 pnfnlt 8478 nltmnf 8479 |
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