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Mirrors > Home > ILE Home > Th. List > sbn | Unicode version |
Description: Negation inside and outside of substitution are equivalent. (Contributed by NM, 5-Aug-1993.) (Proof rewritten by Jim Kingdon, 3-Feb-2018.) |
Ref | Expression |
---|---|
sbn |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | sbnv 1823 |
. . . 4
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2 | 1 | sbbii 1702 |
. . 3
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3 | sbnv 1823 |
. . 3
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4 | 2, 3 | bitri 183 |
. 2
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5 | ax-17 1471 |
. . . 4
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6 | 5 | hbn 1596 |
. . 3
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7 | 6 | sbco2v 1876 |
. 2
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8 | 5 | sbco2v 1876 |
. . 3
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9 | 8 | notbii 632 |
. 2
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10 | 4, 7, 9 | 3bitr3i 209 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-in1 582 ax-in2 583 ax-io 668 ax-5 1388 ax-7 1389 ax-gen 1390 ax-ie1 1434 ax-ie2 1435 ax-8 1447 ax-10 1448 ax-11 1449 ax-i12 1450 ax-4 1452 ax-17 1471 ax-i9 1475 ax-ial 1479 ax-i5r 1480 |
This theorem depends on definitions: df-bi 116 df-tru 1299 df-fal 1302 df-nf 1402 df-sb 1700 |
This theorem is referenced by: sbcng 2893 difab 3284 rabeq0 3331 abeq0 3332 ssfirab 6723 |
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