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Mirrors > Home > ILE Home > Th. List > Mathboxes > strcollnft | Unicode version |
Description: Closed form of strcollnf 10780. Version of ax-strcoll 10777 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 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | strcoll2 10778 | . 2 | |
2 | nfnf1 1476 | . . . . 5 | |
3 | 2 | nfal 1508 | . . . 4 |
4 | 3 | nfal 1508 | . . 3 |
5 | nfa2 1511 | . . . 4 | |
6 | nfvd 1462 | . . . . 5 | |
7 | nfa1 1474 | . . . . . . . 8 | |
8 | nfcvd 2220 | . . . . . . . 8 | |
9 | sp 1441 | . . . . . . . 8 | |
10 | 7, 8, 9 | nfrexdxy 2399 | . . . . . . 7 |
11 | 10 | sps 1470 | . . . . . 6 |
12 | 11 | alcoms 1405 | . . . . 5 |
13 | 6, 12 | nfbid 1520 | . . . 4 |
14 | 5, 13 | nfald 1683 | . . 3 |
15 | nfv 1461 | . . . . . 6 | |
16 | 5, 15 | nfan 1497 | . . . . 5 |
17 | elequ2 1641 | . . . . . . 7 | |
18 | 17 | adantl 271 | . . . . . 6 |
19 | 18 | bibi1d 231 | . . . . 5 |
20 | 16, 19 | albid 1546 | . . . 4 |
21 | 20 | ex 113 | . . 3 |
22 | 4, 14, 21 | cbvexd 1843 | . 2 |
23 | 1, 22 | syl5ib 152 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wal 1282 wnf 1389 wex 1421 wral 2348 wrex 2349 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-14 1445 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-strcoll 10777 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 |
This theorem is referenced by: strcollnf 10780 |
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