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Mirrors > Home > ILE Home > Th. List > elxp | Unicode version |
Description: Membership in a cross product. (Contributed by NM, 4-Jul-1994.) |
Ref | Expression |
---|---|
elxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xp 4545 | . . 3 | |
2 | 1 | eleq2i 2206 | . 2 |
3 | elopab 4180 | . 2 | |
4 | 2, 3 | bitri 183 | 1 |
Colors of variables: wff set class |
Syntax hints: wa 103 wb 104 wceq 1331 wex 1468 wcel 1480 cop 3530 copab 3988 cxp 4537 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2121 ax-sep 4046 ax-pow 4098 ax-pr 4131 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-v 2688 df-un 3075 df-in 3077 df-ss 3084 df-pw 3512 df-sn 3533 df-pr 3534 df-op 3536 df-opab 3990 df-xp 4545 |
This theorem is referenced by: elxp2 4557 0nelxp 4567 0nelelxp 4568 rabxp 4576 elxp3 4593 elvv 4601 elvvv 4602 0xp 4619 xpmlem 4959 elxp4 5026 elxp5 5027 dfco2a 5039 opabex3d 6019 opabex3 6020 xp1st 6063 xp2nd 6064 poxp 6129 xpsnen 6715 xpcomco 6720 xpassen 6724 nqnq0pi 7246 fsum2dlemstep 11203 |
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