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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 110 | . 2 ⊢ ((𝜓 ∧ 𝜑) → 𝜑) | |
3 | 1, 2 | mto 662 | 1 ⊢ ¬ (𝜓 ∧ 𝜑) |
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-ia2 107 ax-in1 614 ax-in2 615 |
This theorem is referenced by: bianfi 947 axnul 4130 fodjum 7146 nninfwlporlemd 7172 2omotaplemap 7258 xrltnr 9781 nltmnf 9790 3lcm2e6woprm 12088 6lcm4e12 12089 subctctexmid 14835 |
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