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Mirrors > Home > ILE Home > Th. List > xpss | Unicode version |
Description: A cross product is included in the ordered pair universe. Exercise 3 of [TakeutiZaring] p. 25. (Contributed by NM, 2-Aug-1994.) |
Ref | Expression |
---|---|
xpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssv 3114 | . 2 | |
2 | ssv 3114 | . 2 | |
3 | xpss12 4641 | . 2 | |
4 | 1, 2, 3 | mp2an 422 | 1 |
Colors of variables: wff set class |
Syntax hints: cvv 2681 wss 3066 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-17 1506 ax-i9 1510 ax-ial 1514 ax-i5r 1515 ax-ext 2119 |
This theorem depends on definitions: df-bi 116 df-nf 1437 df-sb 1736 df-clab 2124 df-cleq 2130 df-clel 2133 df-nfc 2268 df-v 2683 df-in 3072 df-ss 3079 df-opab 3985 df-xp 4540 |
This theorem is referenced by: relxp 4643 eqbrrdva 4704 relrelss 5060 funinsn 5167 eqopi 6063 op1steq 6070 dfoprab4 6083 f1od2 6125 frecuzrdgtcl 10178 frecuzrdgfunlem 10185 upxp 12430 |
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