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Mirrors > Home > ILE Home > Th. List > rabxp | Unicode version |
Description: Membership in a class builder restricted to a cross product. (Contributed by NM, 20-Feb-2014.) |
Ref | Expression |
---|---|
rabxp.1 |
Ref | Expression |
---|---|
rabxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxp 4615 | . . . . 5 | |
2 | 1 | anbi1i 454 | . . . 4 |
3 | 19.41vv 1890 | . . . 4 | |
4 | anass 399 | . . . . . 6 | |
5 | rabxp.1 | . . . . . . . . 9 | |
6 | 5 | anbi2d 460 | . . . . . . . 8 |
7 | df-3an 969 | . . . . . . . 8 | |
8 | 6, 7 | bitr4di 197 | . . . . . . 7 |
9 | 8 | pm5.32i 450 | . . . . . 6 |
10 | 4, 9 | bitri 183 | . . . . 5 |
11 | 10 | 2exbii 1593 | . . . 4 |
12 | 2, 3, 11 | 3bitr2i 207 | . . 3 |
13 | 12 | abbii 2280 | . 2 |
14 | df-rab 2451 | . 2 | |
15 | df-opab 4038 | . 2 | |
16 | 13, 14, 15 | 3eqtr4i 2195 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 w3a 967 wceq 1342 wex 1479 wcel 2135 cab 2150 crab 2446 cop 3573 copab 4036 cxp 4596 |
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 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-14 2138 ax-ext 2146 ax-sep 4094 ax-pow 4147 ax-pr 4181 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-rab 2451 df-v 2723 df-un 3115 df-in 3117 df-ss 3124 df-pw 3555 df-sn 3576 df-pr 3577 df-op 3579 df-opab 4038 df-xp 4604 |
This theorem is referenced by: (None) |
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