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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 1899 |
. . . 4
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2 | 1 | sbbii 1775 |
. . 3
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3 | sbnv 1899 |
. . 3
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4 | 2, 3 | bitri 184 |
. 2
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5 | ax-17 1536 |
. . . 4
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6 | 5 | hbn 1664 |
. . 3
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7 | 6 | sbco2vh 1956 |
. 2
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8 | 5 | sbco2vh 1956 |
. . 3
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9 | 8 | notbii 669 |
. 2
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10 | 4, 7, 9 | 3bitr3i 210 |
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 106 ax-ia2 107 ax-ia3 108 ax-in1 615 ax-in2 616 ax-io 710 ax-5 1457 ax-7 1458 ax-gen 1459 ax-ie1 1503 ax-ie2 1504 ax-8 1514 ax-10 1515 ax-11 1516 ax-i12 1517 ax-4 1520 ax-17 1536 ax-i9 1540 ax-ial 1544 ax-i5r 1545 |
This theorem depends on definitions: df-bi 117 df-tru 1366 df-fal 1369 df-nf 1471 df-sb 1773 |
This theorem is referenced by: sbcng 3017 difab 3418 rabeq0 3466 abeq0 3467 ssfirab 6950 |
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