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Mirrors > Home > ILE Home > Th. List > Mathboxes > strcollnft | Unicode version |
Description: Closed form of strcollnf 13354. (Contributed by BJ, 21-Oct-2019.) |
Ref | Expression |
---|---|
strcollnft |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strcoll2 13352 |
. 2
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2 | nfnf1 1524 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() | |
3 | 2 | nfal 1556 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
4 | 3 | nfal 1556 |
. . 3
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
5 | nfa1 1522 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
6 | nfcvd 2283 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
7 | nfa1 1522 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
8 | 7 | nfal 1556 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
9 | nfcvd 2283 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
10 | sp 1489 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
11 | 10 | sps 1518 |
. . . . . 6
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12 | 8, 9, 11 | nfrexdxy 2471 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
13 | 5, 6, 12 | nfraldxy 2470 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
14 | 5, 6, 11 | nfrexdxy 2471 |
. . . . 5
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
15 | 8, 9, 14 | nfraldxy 2470 |
. . . 4
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
16 | 13, 15 | nfand 1548 |
. . 3
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17 | nfv 1509 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 5, 17 | nfan 1545 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
19 | rexeq 2630 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
20 | 19 | adantl 275 |
. . . . . 6
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21 | 18, 20 | ralbid 2436 |
. . . . 5
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22 | nfv 1509 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() | |
23 | 8, 22 | nfan 1545 |
. . . . . 6
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
24 | eleq2 2204 |
. . . . . . . 8
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
25 | 24 | adantl 275 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
26 | 25 | imbi1d 230 |
. . . . . 6
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27 | 23, 26 | ralbid2 2442 |
. . . . 5
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28 | 21, 27 | anbi12d 465 |
. . . 4
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29 | 28 | ex 114 |
. . 3
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30 | 4, 16, 29 | cbvexd 1900 |
. 2
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31 | 1, 30 | syl5ib 153 |
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 105 ax-ia2 106 ax-ia3 107 ax-io 699 ax-5 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-10 1484 ax-11 1485 ax-i12 1486 ax-bndl 1487 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 ax-strcoll 13351 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-cleq 2133 df-clel 2136 df-nfc 2271 df-ral 2422 df-rex 2423 |
This theorem is referenced by: strcollnf 13354 |
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