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Mirrors > Home > ILE Home > Th. List > unixpss | Unicode version |
Description: The double class union of a cross product is included in the union of its arguments. (Contributed by NM, 16-Sep-2006.) |
Ref | Expression |
---|---|
unixpss |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | xpsspw 4450 | . . . . 5 | |
2 | 1 | unissi 3603 | . . . 4 |
3 | unipw 3953 | . . . 4 | |
4 | 2, 3 | sseqtri 2977 | . . 3 |
5 | 4 | unissi 3603 | . 2 |
6 | unipw 3953 | . 2 | |
7 | 5, 6 | sseqtri 2977 | 1 |
Colors of variables: wff set class |
Syntax hints: cun 2915 wss 2917 cpw 3359 cuni 3580 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-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-i5r 1428 ax-ext 2022 ax-sep 3875 ax-pow 3927 |
This theorem depends on definitions: df-bi 110 df-3an 887 df-tru 1246 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-nfc 2167 df-v 2559 df-un 2922 df-in 2924 df-ss 2931 df-pw 3361 df-sn 3381 df-pr 3382 df-op 3384 df-uni 3581 df-opab 3819 df-xp 4351 |
This theorem is referenced by: relfld 4846 |
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