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Mirrors > Home > ILE Home > Th. List > nbn | Unicode version |
Description: The negation of a wff is equivalent to the wff's equivalence to falsehood. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
Ref | Expression |
---|---|
nbn.1 |
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Ref | Expression |
---|---|
nbn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nbn.1 |
. . 3
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2 | bibif 688 |
. . 3
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3 | 1, 2 | ax-mp 5 |
. 2
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4 | 3 | bicomi 131 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 604 ax-in2 605 |
This theorem depends on definitions: df-bi 116 |
This theorem is referenced by: nbn3 690 nbfal 1343 n0rf 3380 eq0 3386 disj 3416 dm0rn0 4764 reldm0 4765 |
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