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Mirrors > Home > ILE Home > Th. List > elvv | Unicode version |
Description: Membership in universal class of ordered pairs. (Contributed by NM, 4-Jul-1994.) |
Ref | Expression |
---|---|
elvv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | elxp 4526 | . 2 | |
2 | vex 2663 | . . . . 5 | |
3 | vex 2663 | . . . . 5 | |
4 | 2, 3 | pm3.2i 270 | . . . 4 |
5 | 4 | biantru 300 | . . 3 |
6 | 5 | 2exbii 1570 | . 2 |
7 | 1, 6 | bitr4i 186 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1316 wex 1453 wcel 1465 cvv 2660 cop 3500 cxp 4507 |
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 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-14 1477 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 ax-sep 4016 ax-pow 4068 ax-pr 4101 |
This theorem depends on definitions: df-bi 116 df-3an 949 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-un 3045 df-in 3047 df-ss 3054 df-pw 3482 df-sn 3503 df-pr 3504 df-op 3506 df-opab 3960 df-xp 4515 |
This theorem is referenced by: elvvv 4572 elvvuni 4573 ssrel 4597 elrel 4611 relop 4659 elreldm 4735 dmsnm 4974 1stval2 6021 2ndval2 6022 dfopab2 6055 dfoprab3s 6056 dftpos4 6128 tpostpos 6129 fundmen 6668 |
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