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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-xp 4458 |
. . 3
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2 | 1 | eleq2i 2155 |
. 2
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3 | elopab 4094 |
. 2
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4 | 2, 3 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-io 666 ax-5 1382 ax-7 1383 ax-gen 1384 ax-ie1 1428 ax-ie2 1429 ax-8 1441 ax-10 1442 ax-11 1443 ax-i12 1444 ax-bndl 1445 ax-4 1446 ax-14 1451 ax-17 1465 ax-i9 1469 ax-ial 1473 ax-i5r 1474 ax-ext 2071 ax-sep 3963 ax-pow 4015 ax-pr 4045 |
This theorem depends on definitions: df-bi 116 df-3an 927 df-tru 1293 df-nf 1396 df-sb 1694 df-clab 2076 df-cleq 2082 df-clel 2085 df-nfc 2218 df-v 2622 df-un 3004 df-in 3006 df-ss 3013 df-pw 3435 df-sn 3456 df-pr 3457 df-op 3459 df-opab 3906 df-xp 4458 |
This theorem is referenced by: elxp2 4470 0nelxp 4479 0nelelxp 4480 rabxp 4488 elxp3 4505 elvv 4513 elvvv 4514 0xp 4531 xpmlem 4865 elxp4 4931 elxp5 4932 dfco2a 4944 opabex3d 5906 opabex3 5907 xp1st 5950 xp2nd 5951 poxp 6011 xpsnen 6591 xpcomco 6596 xpassen 6600 nqnq0pi 7058 fsum2dlemstep 10889 |
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