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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpss 4605 |
. 2
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2 | df-rel 4504 |
. 2
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3 | 1, 2 | mpbir 145 |
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 681 ax-5 1404 ax-7 1405 ax-gen 1406 ax-ie1 1450 ax-ie2 1451 ax-8 1463 ax-10 1464 ax-11 1465 ax-i12 1466 ax-bndl 1467 ax-4 1468 ax-17 1487 ax-i9 1491 ax-ial 1495 ax-i5r 1496 ax-ext 2095 |
This theorem depends on definitions: df-bi 116 df-nf 1418 df-sb 1717 df-clab 2100 df-cleq 2106 df-clel 2109 df-nfc 2242 df-v 2657 df-in 3041 df-ss 3048 df-opab 3948 df-xp 4503 df-rel 4504 |
This theorem is referenced by: xpiindim 4634 eliunxp 4636 opeliunxp2 4637 relres 4803 codir 4883 qfto 4884 cnvcnv 4947 dfco2 4994 unixpm 5030 ressn 5035 fliftcnv 5648 fliftfun 5649 opeliunxp2f 6087 reltpos 6099 tpostpos 6113 tposfo 6120 tposf 6121 swoer 6409 xpider 6452 erinxp 6455 xpcomf1o 6670 ltrel 7744 lerel 7746 fisumcom2 11093 txuni2 12261 txdis1cn 12283 xmeter 12419 reldvg 12597 |
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