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Mirrors > Home > ILE Home > Th. List > intnanr | GIF version |
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 3-Apr-1995.) |
Ref | Expression |
---|---|
intnan.1 | ⊢ ¬ φ |
Ref | Expression |
---|---|
intnanr | ⊢ ¬ (φ ∧ ψ) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intnan.1 | . 2 ⊢ ¬ φ | |
2 | simpl 102 | . 2 ⊢ ((φ ∧ ψ) → φ) | |
3 | 1, 2 | mto 587 | 1 ⊢ ¬ (φ ∧ ψ) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∧ wa 97 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-in1 544 ax-in2 545 |
This theorem is referenced by: rab0 3240 co02 4777 frec0g 5922 xrltnr 8471 pnfnlt 8478 nltmnf 8479 |
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