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Mirrors > Home > ILE Home > Th. List > Mathboxes > strcollnft | Unicode version |
Description: Closed form of strcollnf 9445. Version of ax-strcoll 9442 with one DV condition removed, the other DV condition replaced by a non-freeness antecedent, and without initial universal quantifier. (Contributed by BJ, 21-Oct-2019.) |
Ref | Expression |
---|---|
strcollnft |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strcoll2 9443 |
. 2
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2 | nfnf1 1433 |
. . . . 5
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3 | 2 | nfal 1465 |
. . . 4
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4 | 3 | nfal 1465 |
. . 3
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5 | nfa2 1468 |
. . . 4
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6 | nfvd 1419 |
. . . . 5
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7 | nfa1 1431 |
. . . . . . . 8
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8 | nfcvd 2176 |
. . . . . . . 8
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9 | sp 1398 |
. . . . . . . 8
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10 | 7, 8, 9 | nfrexdxy 2351 |
. . . . . . 7
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11 | 10 | sps 1427 |
. . . . . 6
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12 | 11 | alcoms 1362 |
. . . . 5
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13 | 6, 12 | nfbid 1477 |
. . . 4
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14 | 5, 13 | nfald 1640 |
. . 3
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15 | nfv 1418 |
. . . . . 6
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16 | 5, 15 | nfan 1454 |
. . . . 5
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17 | elequ2 1598 |
. . . . . . 7
![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() | |
18 | 17 | adantl 262 |
. . . . . 6
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19 | 18 | bibi1d 222 |
. . . . 5
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20 | 16, 19 | albid 1503 |
. . . 4
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21 | 20 | ex 108 |
. . 3
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22 | 4, 14, 21 | cbvexd 1799 |
. 2
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23 | 1, 22 | syl5ib 143 |
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-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-bndl 1396 ax-4 1397 ax-14 1402 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 ax-strcoll 9442 |
This theorem depends on definitions: df-bi 110 df-tru 1245 df-nf 1347 df-sb 1643 df-cleq 2030 df-clel 2033 df-nfc 2164 df-ral 2305 df-rex 2306 |
This theorem is referenced by: strcollnf 9445 |
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