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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 4736 |
. 2
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2 | df-rel 4635 |
. 2
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3 | 1, 2 | mpbir 146 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 |
This theorem depends on definitions: df-bi 117 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-v 2741 df-in 3137 df-ss 3144 df-opab 4067 df-xp 4634 df-rel 4635 |
This theorem is referenced by: xpiindim 4766 eliunxp 4768 opeliunxp2 4769 relres 4937 restidsing 4965 codir 5019 qfto 5020 cnvcnv 5083 dfco2 5130 unixpm 5166 ressn 5171 fliftcnv 5798 fliftfun 5799 opeliunxp2f 6241 reltpos 6253 tpostpos 6267 tposfo 6274 tposf 6275 swoer 6565 xpider 6608 erinxp 6611 xpcomf1o 6827 ltrel 8021 lerel 8023 fisumcom2 11448 fprodcom2fi 11636 txuni2 13841 txdis1cn 13863 xmeter 14021 reldvg 14233 |
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