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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 4758 |
. 2
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4 | 1, 2, 3 | mp2an 426 |
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 710 ax-5 1458 ax-7 1459 ax-gen 1460 ax-ie1 1504 ax-ie2 1505 ax-8 1515 ax-10 1516 ax-11 1517 ax-i12 1518 ax-bndl 1520 ax-4 1521 ax-17 1537 ax-i9 1541 ax-ial 1545 ax-i5r 1546 ax-13 2162 ax-14 2163 ax-ext 2171 ax-sep 4136 ax-pow 4192 ax-pr 4227 ax-un 4451 |
This theorem depends on definitions: df-bi 117 df-3an 982 df-tru 1367 df-nf 1472 df-sb 1774 df-clab 2176 df-cleq 2182 df-clel 2185 df-nfc 2321 df-rex 2474 df-v 2754 df-un 3148 df-in 3150 df-ss 3157 df-pw 3592 df-sn 3613 df-pr 3614 df-op 3616 df-uni 3825 df-opab 4080 df-xp 4650 |
This theorem is referenced by: oprabex 6154 oprabex3 6155 mpoexw 6239 fnpm 6683 mapsnf1o2 6723 xpsnen 6848 endisj 6851 xpcomen 6854 xpassen 6857 xpmapenlem 6878 0ct 7137 exmidomni 7171 exmidfodomrlemim 7231 2omotaplemst 7288 enqex 7390 nqex 7393 enq0ex 7469 nq0ex 7470 npex 7503 enrex 7767 addvalex 7874 axcnex 7889 addex 9683 mulex 9684 ixxex 9931 fxnn0nninf 10471 inftonninf 10474 shftfval 10865 qnumval 12220 qdenval 12221 qnnen 12485 prdsex 12777 znval 13949 znle 13950 znbaslemnn 13952 fnpsr 13962 txuni2 14233 txbas 14235 eltx 14236 txcnp 14248 txcnmpt 14250 txrest 14253 txlm 14256 reldvg 14625 |
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