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Mirrors > Home > ILE Home > Th. List > elxp2 | Unicode version |
Description: Membership in a cross product. (Contributed by NM, 23-Feb-2004.) |
Ref | Expression |
---|---|
elxp2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2448 | . . . 4 | |
2 | r19.42v 2621 | . . . 4 | |
3 | an13 553 | . . . . 5 | |
4 | 3 | exbii 1592 | . . . 4 |
5 | 1, 2, 4 | 3bitr3i 209 | . . 3 |
6 | 5 | exbii 1592 | . 2 |
7 | df-rex 2448 | . 2 | |
8 | elxp 4615 | . 2 | |
9 | 6, 7, 8 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1342 wex 1479 wcel 2135 wrex 2443 cop 3573 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-rex 2448 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: opelxp 4628 xpiundi 4656 xpiundir 4657 ssrel2 4688 f1o2ndf1 6187 xpdom2 6788 elreal 7760 |
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