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Mirrors > Home > ILE Home > Th. List > dfnot | Unicode version |
Description: Given falsum, we can define the negation of a wff as the statement that a contradiction follows from assuming . (Contributed by Mario Carneiro, 9-Feb-2017.) (Proof shortened by Wolf Lammen, 21-Jul-2019.) |
Ref | Expression |
---|---|
dfnot |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | fal 1323 | . 2 | |
2 | mtt 659 | . 2 | |
3 | 1, 2 | ax-mp 5 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wb 104 wfal 1321 |
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 588 ax-in2 589 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-fal 1322 |
This theorem is referenced by: inegd 1335 pclem6 1337 alnex 1460 alexim 1609 difin 3283 indifdir 3302 recvguniq 10735 bj-axempty2 13019 |
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