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Mirrors > Home > ILE Home > Th. List > dfss4st | Unicode version |
Description: Subclass defined in terms of class difference. (Contributed by NM, 22-Mar-1998.) (Proof shortened by Andrew Salmon, 26-Jun-2011.) |
Ref | Expression |
---|---|
dfss4st | STAB |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eleq1w 2225 | . . . 4 | |
2 | 1 | stbid 822 | . . 3 STAB STAB |
3 | 2 | cbvalv 1904 | . 2 STAB STAB |
4 | sseqin2 3336 | . . 3 | |
5 | nfa1 1528 | . . . . 5 STAB | |
6 | nfcv 2306 | . . . . 5 | |
7 | nfcv 2306 | . . . . 5 | |
8 | eldif 3120 | . . . . . . 7 | |
9 | eldif 3120 | . . . . . . . . . 10 | |
10 | 9 | notbii 658 | . . . . . . . . 9 |
11 | 10 | anbi2i 453 | . . . . . . . 8 |
12 | elin 3300 | . . . . . . . . . 10 | |
13 | abai 550 | . . . . . . . . . 10 | |
14 | 12, 13 | bitri 183 | . . . . . . . . 9 |
15 | imanst 878 | . . . . . . . . . 10 STAB | |
16 | 15 | anbi2d 460 | . . . . . . . . 9 STAB |
17 | 14, 16 | syl5bb 191 | . . . . . . . 8 STAB |
18 | 11, 17 | bitr4id 198 | . . . . . . 7 STAB |
19 | 8, 18 | syl5bb 191 | . . . . . 6 STAB |
20 | 19 | sps 1524 | . . . . 5 STAB |
21 | 5, 6, 7, 20 | eqrd 3155 | . . . 4 STAB |
22 | 21 | eqeq1d 2173 | . . 3 STAB |
23 | 4, 22 | bitr4id 198 | . 2 STAB |
24 | 3, 23 | sylbi 120 | 1 STAB |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 STAB wstab 820 wal 1340 wceq 1342 wcel 2135 cdif 3108 cin 3110 wss 3111 |
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-in1 604 ax-in2 605 ax-io 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-stab 821 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-v 2723 df-dif 3113 df-in 3117 df-ss 3124 |
This theorem is referenced by: sbthlemi3 6915 |
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