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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 4617 | . 2 | |
2 | df-rel 4516 | . 2 | |
3 | 1, 2 | mpbir 145 | 1 |
Colors of variables: wff set class |
Syntax hints: cvv 2660 wss 3041 cxp 4507 wrel 4514 |
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-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-v 2662 df-in 3047 df-ss 3054 df-opab 3960 df-xp 4515 df-rel 4516 |
This theorem is referenced by: xpiindim 4646 eliunxp 4648 opeliunxp2 4649 relres 4817 codir 4897 qfto 4898 cnvcnv 4961 dfco2 5008 unixpm 5044 ressn 5049 fliftcnv 5664 fliftfun 5665 opeliunxp2f 6103 reltpos 6115 tpostpos 6129 tposfo 6136 tposf 6137 swoer 6425 xpider 6468 erinxp 6471 xpcomf1o 6687 ltrel 7794 lerel 7796 fisumcom2 11162 txuni2 12336 txdis1cn 12358 xmeter 12516 reldvg 12728 |
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