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Mirrors > Home > NFE Home > Th. List > iinrab2 | Unicode version |
Description: Indexed intersection of a restricted class builder. (Contributed by NM, 6-Dec-2011.) |
Ref | Expression |
---|---|
iinrab2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | iineq1 3983 | . . . . . 6 | |
2 | 0iin 4024 | . . . . . 6 | |
3 | 1, 2 | syl6eq 2401 | . . . . 5 |
4 | 3 | ineq1d 3456 | . . . 4 |
5 | incom 3448 | . . . . 5 | |
6 | inv1 3577 | . . . . 5 | |
7 | 5, 6 | eqtri 2373 | . . . 4 |
8 | 4, 7 | syl6eq 2401 | . . 3 |
9 | rzal 3651 | . . . 4 | |
10 | rabid2 2788 | . . . . 5 | |
11 | ralcom 2771 | . . . . 5 | |
12 | 10, 11 | bitr2i 241 | . . . 4 |
13 | 9, 12 | sylib 188 | . . 3 |
14 | 8, 13 | eqtrd 2385 | . 2 |
15 | iinrab 4028 | . . . 4 | |
16 | 15 | ineq1d 3456 | . . 3 |
17 | ssrab2 3351 | . . . 4 | |
18 | dfss 3260 | . . . 4 | |
19 | 17, 18 | mpbi 199 | . . 3 |
20 | 16, 19 | syl6eqr 2403 | . 2 |
21 | 14, 20 | pm2.61ine 2592 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wceq 1642 wne 2516 wral 2614 crab 2618 cvv 2859 cin 3208 wss 3257 c0 3550 ciin 3970 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-nan 1288 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2478 df-ne 2518 df-ral 2619 df-rab 2623 df-v 2861 df-nin 3211 df-compl 3212 df-in 3213 df-dif 3215 df-ss 3259 df-nul 3551 df-iin 3972 |
This theorem is referenced by: (None) |
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