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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 2146 | . . . . . . . . . 10 | |
2 | 1 | anbi2d 459 | . . . . . . . . 9 |
3 | 2 | exbidv 1797 | . . . . . . . 8 |
4 | 3 | cbvabv 2264 | . . . . . . 7 |
5 | intab.2 | . . . . . . 7 | |
6 | 4, 5 | eqeltri 2212 | . . . . . 6 |
7 | nfe1 1472 | . . . . . . . . 9 | |
8 | 7 | nfab 2286 | . . . . . . . 8 |
9 | 8 | nfeq2 2293 | . . . . . . 7 |
10 | eleq2 2203 | . . . . . . . 8 | |
11 | 10 | imbi2d 229 | . . . . . . 7 |
12 | 9, 11 | albid 1594 | . . . . . 6 |
13 | 6, 12 | elab 2828 | . . . . 5 |
14 | 19.8a 1569 | . . . . . . . . 9 | |
15 | 14 | ex 114 | . . . . . . . 8 |
16 | 15 | alrimiv 1846 | . . . . . . 7 |
17 | intab.1 | . . . . . . . 8 | |
18 | 17 | sbc6 2934 | . . . . . . 7 |
19 | 16, 18 | sylibr 133 | . . . . . 6 |
20 | df-sbc 2910 | . . . . . 6 | |
21 | 19, 20 | sylib 121 | . . . . 5 |
22 | 13, 21 | mpgbir 1429 | . . . 4 |
23 | intss1 3786 | . . . 4 | |
24 | 22, 23 | ax-mp 5 | . . 3 |
25 | 19.29r 1600 | . . . . . . . 8 | |
26 | simplr 519 | . . . . . . . . . 10 | |
27 | pm3.35 344 | . . . . . . . . . . 11 | |
28 | 27 | adantlr 468 | . . . . . . . . . 10 |
29 | 26, 28 | eqeltrd 2216 | . . . . . . . . 9 |
30 | 29 | exlimiv 1577 | . . . . . . . 8 |
31 | 25, 30 | syl 14 | . . . . . . 7 |
32 | 31 | ex 114 | . . . . . 6 |
33 | 32 | alrimiv 1846 | . . . . 5 |
34 | vex 2689 | . . . . . 6 | |
35 | 34 | elintab 3782 | . . . . 5 |
36 | 33, 35 | sylibr 133 | . . . 4 |
37 | 36 | abssi 3172 | . . 3 |
38 | 24, 37 | eqssi 3113 | . 2 |
39 | 38, 4 | eqtri 2160 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wal 1329 wceq 1331 wex 1468 wcel 1480 cab 2125 cvv 2686 wsbc 2909 wss 3071 cint 3771 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-sbc 2910 df-in 3077 df-ss 3084 df-int 3772 |
This theorem is referenced by: (None) |
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