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Mirrors > Home > ILE Home > Th. List > relxp | Unicode version |
Description: A cross product is a relation. Theorem 3.13(i) of [Monk1] p. 37. (Contributed by NM, 2-Aug-1994.) |
Ref | Expression |
---|---|
relxp |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpss 4464 | . 2 | |
2 | df-rel 4370 | . 2 | |
3 | 1, 2 | mpbir 144 | 1 |
Colors of variables: wff set class |
Syntax hints: cvv 2601 wss 2973 cxp 4361 wrel 4368 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-v 2603 df-in 2979 df-ss 2986 df-opab 3840 df-xp 4369 df-rel 4370 |
This theorem is referenced by: xpiindim 4491 eliunxp 4493 opeliunxp2 4494 relres 4657 codir 4733 qfto 4734 cnvcnv 4793 dfco2 4840 unixpm 4873 ressn 4878 fliftcnv 5455 fliftfun 5456 reltpos 5888 tpostpos 5902 tposfo 5909 tposf 5910 swoer 6157 xpiderm 6200 erinxp 6203 xpcomf1o 6322 ltrel 7174 lerel 7176 |
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