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Mirrors > Home > ILE Home > Th. List > intnan | GIF version |
Description: Introduction of conjunct inside of a contradiction. (Contributed by NM, 16-Sep-1993.) |
Ref | Expression |
---|---|
intnan.1 | ⊢ ¬ 𝜑 |
Ref | Expression |
---|---|
intnan | ⊢ ¬ (𝜓 ∧ 𝜑) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | intnan.1 | . 2 ⊢ ¬ 𝜑 | |
2 | simpr 109 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑) | |
3 | 1, 2 | mto 624 | 1 ⊢ ¬ (𝜓 ∧ 𝜑) |
Colors of variables: wff set class |
Syntax hints: ¬ wn 3 ∧ wa 103 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia2 106 ax-in1 580 ax-in2 581 |
This theorem is referenced by: bianfi 894 axnul 3972 fodjuomnilemm 6864 xrltnr 9313 nltmnf 9321 3lcm2e6woprm 11409 6lcm4e12 11410 |
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