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Mirrors > Home > ILE Home > Th. List > xpex | Unicode version |
Description: The cross product of two sets is a set. Proposition 6.2 of [TakeutiZaring] p. 23. (Contributed by NM, 14-Aug-1994.) |
Ref | Expression |
---|---|
xpex.1 |
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xpex.2 |
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Ref | Expression |
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xpex |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpex.1 |
. 2
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2 | xpex.2 |
. 2
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3 | xpexg 4591 |
. 2
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4 | 1, 2, 3 | mp2an 420 |
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 671 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-10 1451 ax-11 1452 ax-i12 1453 ax-bndl 1454 ax-4 1455 ax-13 1459 ax-14 1460 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-i5r 1483 ax-ext 2082 ax-sep 3986 ax-pow 4038 ax-pr 4069 ax-un 4293 |
This theorem depends on definitions: df-bi 116 df-3an 932 df-tru 1302 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-nfc 2229 df-rex 2381 df-v 2643 df-un 3025 df-in 3027 df-ss 3034 df-pw 3459 df-sn 3480 df-pr 3481 df-op 3483 df-uni 3684 df-opab 3930 df-xp 4483 |
This theorem is referenced by: oprabex 5957 oprabex3 5958 fnpm 6480 mapsnf1o2 6520 xpsnen 6644 endisj 6647 xpcomen 6650 xpassen 6653 xpmapenlem 6672 0ct 6907 exmidomni 6926 exmidfodomrlemim 6966 enqex 7069 nqex 7072 enq0ex 7148 nq0ex 7149 npex 7182 enrex 7433 addvalex 7531 axcnex 7546 ixxex 9523 fxnn0nninf 10052 inftonninf 10055 shftfval 10434 qnumval 11655 qdenval 11656 qnnen 11736 txuni2 12206 txbas 12208 eltx 12209 txcnp 12221 txcnmpt 12223 txrest 12226 txlm 12229 reldvg 12521 |
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