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Mirrors > Home > ILE Home > Th. List > xpss12 | Unicode version |
Description: Subset theorem for cross product. Generalization of Theorem 101 of [Suppes] p. 52. (Contributed by NM, 26-Aug-1995.) (Proof shortened by Andrew Salmon, 27-Aug-2011.) |
Ref | Expression |
---|---|
xpss12 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | ssel 2939 | . . . 4 | |
2 | ssel 2939 | . . . 4 | |
3 | 1, 2 | im2anan9 530 | . . 3 |
4 | 3 | ssopab2dv 4015 | . 2 |
5 | df-xp 4351 | . 2 | |
6 | df-xp 4351 | . 2 | |
7 | 4, 5, 6 | 3sstr4g 2986 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 97 wcel 1393 wss 2917 copab 3817 cxp 4343 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-io 630 ax-5 1336 ax-7 1337 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-10 1396 ax-11 1397 ax-i12 1398 ax-bndl 1399 ax-4 1400 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 |
This theorem depends on definitions: df-bi 110 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-in 2924 df-ss 2931 df-opab 3819 df-xp 4351 |
This theorem is referenced by: xpss 4446 xpss1 4448 xpss2 4449 djussxp 4481 ssxpbm 4756 ssrnres 4763 cossxp 4843 relrelss 4844 fssxp 5058 oprabss 5590 dmaddpi 6423 dmmulpi 6424 rexpssxrxp 7070 ltrelxr 7080 dfz2 8313 |
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