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Mirrors > Home > ILE Home > Th. List > intmin4 | Unicode version |
Description: Elimination of a conjunct in a class intersection. (Contributed by NM, 31-Jul-2006.) |
Ref | Expression |
---|---|
intmin4 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssintab 3826 | . . . 4 | |
2 | simpr 109 | . . . . . . . 8 | |
3 | ancr 319 | . . . . . . . 8 | |
4 | 2, 3 | impbid2 142 | . . . . . . 7 |
5 | 4 | imbi1d 230 | . . . . . 6 |
6 | 5 | alimi 1435 | . . . . 5 |
7 | albi 1448 | . . . . 5 | |
8 | 6, 7 | syl 14 | . . . 4 |
9 | 1, 8 | sylbi 120 | . . 3 |
10 | vex 2715 | . . . 4 | |
11 | 10 | elintab 3820 | . . 3 |
12 | 10 | elintab 3820 | . . 3 |
13 | 9, 11, 12 | 3bitr4g 222 | . 2 |
14 | 13 | eqrdv 2155 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wal 1333 wceq 1335 wcel 2128 cab 2143 wss 3102 cint 3809 |
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 699 ax-5 1427 ax-7 1428 ax-gen 1429 ax-ie1 1473 ax-ie2 1474 ax-8 1484 ax-10 1485 ax-11 1486 ax-i12 1487 ax-bndl 1489 ax-4 1490 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2139 |
This theorem depends on definitions: df-bi 116 df-tru 1338 df-nf 1441 df-sb 1743 df-clab 2144 df-cleq 2150 df-clel 2153 df-nfc 2288 df-ral 2440 df-v 2714 df-in 3108 df-ss 3115 df-int 3810 |
This theorem is referenced by: (None) |
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