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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 109 | . 2 ⊢ ((𝜑 ∧ 𝜓) → 𝜑) | |
3 | 1, 2 | mto 662 | 1 ⊢ ¬ (𝜑 ∧ 𝜓) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∧ wa 104 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-in1 614 ax-in2 615 |
This theorem is referenced by: rab0 3451 co02 5142 frec0g 6397 djulclb 7053 xrltnr 9777 pnfnlt 9785 nltmnf 9786 0g0 12749 if0ab 14439 |
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