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Mirrors > Home > ILE Home > Th. List > basis2 | Unicode version |
Description: Property of a basis. (Contributed by NM, 17-Jul-2006.) |
Ref | Expression |
---|---|
basis2 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | isbasis2g 12215 | . . . . 5 | |
2 | 1 | ibi 175 | . . . 4 |
3 | ineq1 3270 | . . . . . . 7 | |
4 | sseq2 3121 | . . . . . . . . . 10 | |
5 | 4 | anbi2d 459 | . . . . . . . . 9 |
6 | 5 | rexbidv 2438 | . . . . . . . 8 |
7 | 6 | raleqbi1dv 2634 | . . . . . . 7 |
8 | 3, 7 | syl 14 | . . . . . 6 |
9 | ineq2 3271 | . . . . . . 7 | |
10 | sseq2 3121 | . . . . . . . . . 10 | |
11 | 10 | anbi2d 459 | . . . . . . . . 9 |
12 | 11 | rexbidv 2438 | . . . . . . . 8 |
13 | 12 | raleqbi1dv 2634 | . . . . . . 7 |
14 | 9, 13 | syl 14 | . . . . . 6 |
15 | 8, 14 | rspc2v 2802 | . . . . 5 |
16 | eleq1 2202 | . . . . . . . 8 | |
17 | 16 | anbi1d 460 | . . . . . . 7 |
18 | 17 | rexbidv 2438 | . . . . . 6 |
19 | 18 | rspccv 2786 | . . . . 5 |
20 | 15, 19 | syl6com 35 | . . . 4 |
21 | 2, 20 | syl 14 | . . 3 |
22 | 21 | expd 256 | . 2 |
23 | 22 | imp43 352 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1331 wcel 1480 wral 2416 wrex 2417 cin 3070 wss 3071 ctb 12212 |
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 2121 |
This theorem depends on definitions: df-bi 116 df-tru 1334 df-nf 1437 df-sb 1736 df-clab 2126 df-cleq 2132 df-clel 2135 df-nfc 2270 df-ral 2421 df-rex 2422 df-v 2688 df-in 3077 df-ss 3084 df-pw 3512 df-uni 3737 df-bases 12213 |
This theorem is referenced by: tgcl 12236 restbasg 12340 txbas 12430 tgioo 12718 |
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