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Mirrors > Home > MPE Home > Th. List > nbn | Structured version Visualization version Unicode version |
Description: The negation of a wff is equivalent to the wff's equivalence to falsehood. (Contributed by NM, 21-Jun-1993.) (Proof shortened by Wolf Lammen, 3-Oct-2013.) |
Ref | Expression |
---|---|
nbn.1 |
Ref | Expression |
---|---|
nbn |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nbn.1 | . . 3 | |
2 | bibif 361 | . . 3 | |
3 | 1, 2 | ax-mp 5 | . 2 |
4 | 3 | bicomi 214 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wn 3 wb 196 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 |
This theorem depends on definitions: df-bi 197 |
This theorem is referenced by: nbn3 363 nbfal 1495 eq0f 3925 n0fOLD 3928 disj 4017 axnulALT 4787 dm0rn0 5342 reldm0 5343 isarchi 29736 |
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