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Mirrors > Home > ILE Home > Th. List > nfsbxyt | Unicode version |
Description: Closed form of nfsbxy 1954. (Contributed by Jim Kingdon, 9-May-2018.) |
Ref | Expression |
---|---|
nfsbxyt |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ax-bndl 1520 |
. 2
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2 | nfs1v 1951 |
. . . . 5
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3 | drsb1 1810 |
. . . . . 6
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4 | 3 | drnf2 1745 |
. . . . 5
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5 | 2, 4 | mpbii 148 |
. . . 4
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6 | 5 | a1d 22 |
. . 3
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7 | a16nf 1877 |
. . . . 5
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8 | 7 | a1d 22 |
. . . 4
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9 | df-nf 1472 |
. . . . . 6
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10 | 9 | albii 1481 |
. . . . 5
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11 | sb5 1899 |
. . . . . . 7
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12 | nfa1 1552 |
. . . . . . . . 9
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13 | nfa1 1552 |
. . . . . . . . 9
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14 | 12, 13 | nfan 1576 |
. . . . . . . 8
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15 | sp 1522 |
. . . . . . . . . 10
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16 | 15 | adantr 276 |
. . . . . . . . 9
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17 | sp 1522 |
. . . . . . . . . 10
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18 | 17 | adantl 277 |
. . . . . . . . 9
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19 | 16, 18 | nfand 1579 |
. . . . . . . 8
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20 | 14, 19 | nfexd 1772 |
. . . . . . 7
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21 | 11, 20 | nfxfrd 1486 |
. . . . . 6
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22 | 21 | ex 115 |
. . . . 5
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23 | 10, 22 | sylbir 135 |
. . . 4
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24 | 8, 23 | jaoi 717 |
. . 3
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25 | 6, 24 | jaoi 717 |
. 2
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26 | 1, 25 | ax-mp 5 |
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-io 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 |
This theorem depends on definitions: df-bi 117 df-nf 1472 df-sb 1774 |
This theorem is referenced by: nfsbt 1988 |
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