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Mirrors > Home > ILE Home > Th. List > nfsbxyt | Unicode version |
Description: Closed form of nfsbxy 1878. (Contributed by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsbxyt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bndl 1454 |
. 2
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2 | nfs1v 1875 |
. . . . 5
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3 | drsb1 1738 |
. . . . . 6
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4 | 3 | drnf2 1680 |
. . . . 5
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5 | 2, 4 | mpbii 147 |
. . . 4
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6 | 5 | a1d 22 |
. . 3
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7 | a16nf 1805 |
. . . . 5
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8 | 7 | a1d 22 |
. . . 4
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9 | df-nf 1405 |
. . . . . 6
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10 | 9 | albii 1414 |
. . . . 5
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11 | sb5 1826 |
. . . . . . 7
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12 | nfa1 1489 |
. . . . . . . . 9
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13 | nfa1 1489 |
. . . . . . . . 9
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14 | 12, 13 | nfan 1512 |
. . . . . . . 8
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15 | sp 1456 |
. . . . . . . . . 10
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16 | 15 | adantr 272 |
. . . . . . . . 9
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17 | sp 1456 |
. . . . . . . . . 10
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18 | 17 | adantl 273 |
. . . . . . . . 9
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19 | 16, 18 | nfand 1515 |
. . . . . . . 8
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20 | 14, 19 | nfexd 1702 |
. . . . . . 7
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21 | 11, 20 | nfxfrd 1419 |
. . . . . 6
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22 | 21 | ex 114 |
. . . . 5
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23 | 10, 22 | sylbir 134 |
. . . 4
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24 | 8, 23 | jaoi 677 |
. . 3
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25 | 6, 24 | jaoi 677 |
. 2
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26 | 1, 25 | ax-mp 7 |
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-io 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 |
This theorem depends on definitions: df-bi 116 df-nf 1405 df-sb 1704 |
This theorem is referenced by: nfsbt 1910 |
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