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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 1765 |
. . . 4
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2 | 1 | sbbii 1645 |
. . 3
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3 | sbnv 1765 |
. . 3
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4 | 2, 3 | bitri 173 |
. 2
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5 | ax-17 1416 |
. . . 4
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6 | 5 | hbn 1541 |
. . 3
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7 | 6 | sbco2v 1818 |
. 2
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8 | 5 | sbco2v 1818 |
. . 3
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9 | 8 | notbii 593 |
. 2
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10 | 4, 7, 9 | 3bitr3i 199 |
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 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-io 629 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-10 1393 ax-11 1394 ax-i12 1395 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-fal 1248 df-nf 1347 df-sb 1643 |
This theorem is referenced by: sbcng 2797 difab 3200 rabeq0 3241 abeq0 3242 |
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