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Mirrors > Home > ILE Home > Th. List > intab | Unicode version |
Description: The intersection of a special case of a class abstraction. may be free in and , which can be thought of a and . (Contributed by NM, 28-Jul-2006.) (Proof shortened by Mario Carneiro, 14-Nov-2016.) |
Ref | Expression |
---|---|
intab.1 | |
intab.2 |
Ref | Expression |
---|---|
intab |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqeq1 2046 | . . . . . . . . . 10 | |
2 | 1 | anbi2d 437 | . . . . . . . . 9 |
3 | 2 | exbidv 1706 | . . . . . . . 8 |
4 | 3 | cbvabv 2161 | . . . . . . 7 |
5 | intab.2 | . . . . . . 7 | |
6 | 4, 5 | eqeltri 2110 | . . . . . 6 |
7 | nfe1 1385 | . . . . . . . . 9 | |
8 | 7 | nfab 2182 | . . . . . . . 8 |
9 | 8 | nfeq2 2189 | . . . . . . 7 |
10 | eleq2 2101 | . . . . . . . 8 | |
11 | 10 | imbi2d 219 | . . . . . . 7 |
12 | 9, 11 | albid 1506 | . . . . . 6 |
13 | 6, 12 | elab 2687 | . . . . 5 |
14 | 19.8a 1482 | . . . . . . . . 9 | |
15 | 14 | ex 108 | . . . . . . . 8 |
16 | 15 | alrimiv 1754 | . . . . . . 7 |
17 | intab.1 | . . . . . . . 8 | |
18 | 17 | sbc6 2789 | . . . . . . 7 |
19 | 16, 18 | sylibr 137 | . . . . . 6 |
20 | df-sbc 2765 | . . . . . 6 | |
21 | 19, 20 | sylib 127 | . . . . 5 |
22 | 13, 21 | mpgbir 1342 | . . . 4 |
23 | intss1 3630 | . . . 4 | |
24 | 22, 23 | ax-mp 7 | . . 3 |
25 | 19.29r 1512 | . . . . . . . 8 | |
26 | simplr 482 | . . . . . . . . . 10 | |
27 | pm3.35 329 | . . . . . . . . . . 11 | |
28 | 27 | adantlr 446 | . . . . . . . . . 10 |
29 | 26, 28 | eqeltrd 2114 | . . . . . . . . 9 |
30 | 29 | exlimiv 1489 | . . . . . . . 8 |
31 | 25, 30 | syl 14 | . . . . . . 7 |
32 | 31 | ex 108 | . . . . . 6 |
33 | 32 | alrimiv 1754 | . . . . 5 |
34 | vex 2560 | . . . . . 6 | |
35 | 34 | elintab 3626 | . . . . 5 |
36 | 33, 35 | sylibr 137 | . . . 4 |
37 | 36 | abssi 3015 | . . 3 |
38 | 24, 37 | eqssi 2961 | . 2 |
39 | 38, 4 | eqtri 2060 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wal 1241 wceq 1243 wex 1381 wcel 1393 cab 2026 cvv 2557 wsbc 2764 wss 2917 cint 3615 |
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 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-sbc 2765 df-in 2924 df-ss 2931 df-int 3616 |
This theorem is referenced by: (None) |
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