Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
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 12590 | . . . . 5 | |
2 | 1 | ibi 175 | . . . 4 |
3 | ineq1 3311 | . . . . . . 7 | |
4 | sseq2 3161 | . . . . . . . . . 10 | |
5 | 4 | anbi2d 460 | . . . . . . . . 9 |
6 | 5 | rexbidv 2465 | . . . . . . . 8 |
7 | 6 | raleqbi1dv 2667 | . . . . . . 7 |
8 | 3, 7 | syl 14 | . . . . . 6 |
9 | ineq2 3312 | . . . . . . 7 | |
10 | sseq2 3161 | . . . . . . . . . 10 | |
11 | 10 | anbi2d 460 | . . . . . . . . 9 |
12 | 11 | rexbidv 2465 | . . . . . . . 8 |
13 | 12 | raleqbi1dv 2667 | . . . . . . 7 |
14 | 9, 13 | syl 14 | . . . . . 6 |
15 | 8, 14 | rspc2v 2838 | . . . . 5 |
16 | eleq1 2227 | . . . . . . . 8 | |
17 | 16 | anbi1d 461 | . . . . . . 7 |
18 | 17 | rexbidv 2465 | . . . . . 6 |
19 | 18 | rspccv 2822 | . . . . 5 |
20 | 15, 19 | syl6com 35 | . . . 4 |
21 | 2, 20 | syl 14 | . . 3 |
22 | 21 | expd 256 | . 2 |
23 | 22 | imp43 353 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1342 wcel 2135 wral 2442 wrex 2443 cin 3110 wss 3111 ctb 12587 |
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 699 ax-5 1434 ax-7 1435 ax-gen 1436 ax-ie1 1480 ax-ie2 1481 ax-8 1491 ax-10 1492 ax-11 1493 ax-i12 1494 ax-bndl 1496 ax-4 1497 ax-17 1513 ax-i9 1517 ax-ial 1521 ax-i5r 1522 ax-ext 2146 |
This theorem depends on definitions: df-bi 116 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rex 2448 df-v 2723 df-in 3117 df-ss 3124 df-pw 3555 df-uni 3784 df-bases 12588 |
This theorem is referenced by: tgcl 12611 restbasg 12715 txbas 12805 tgioo 13093 |
Copyright terms: Public domain | W3C validator |