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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 | |
xpex.2 |
Ref | Expression |
---|---|
xpex |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpex.1 | . 2 | |
2 | xpex.2 | . 2 | |
3 | xpexg 4648 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: wcel 1480 cvv 2681 cxp 4532 |
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 698 ax-5 1423 ax-7 1424 ax-gen 1425 ax-ie1 1469 ax-ie2 1470 ax-8 1482 ax-10 1483 ax-11 1484 ax-i12 1485 ax-bndl 1486 ax-4 1487 ax-13 1491 ax-14 1492 ax-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 ax-sep 4041 ax-pow 4093 ax-pr 4126 ax-un 4350 |
This theorem depends on definitions: df-bi 116 df-3an 964 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-rex 2420 df-v 2683 df-un 3070 df-in 3072 df-ss 3079 df-pw 3507 df-sn 3528 df-pr 3529 df-op 3531 df-uni 3732 df-opab 3985 df-xp 4540 |
This theorem is referenced by: oprabex 6019 oprabex3 6020 fnpm 6543 mapsnf1o2 6583 xpsnen 6708 endisj 6711 xpcomen 6714 xpassen 6717 xpmapenlem 6736 0ct 6985 exmidomni 7007 exmidfodomrlemim 7050 enqex 7161 nqex 7164 enq0ex 7240 nq0ex 7241 npex 7274 enrex 7538 addvalex 7645 axcnex 7660 ixxex 9675 fxnn0nninf 10204 inftonninf 10207 shftfval 10586 qnumval 11852 qdenval 11853 qnnen 11933 txuni2 12414 txbas 12416 eltx 12417 txcnp 12429 txcnmpt 12431 txrest 12434 txlm 12437 reldvg 12806 |
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