Intuitionistic Logic Explorer |
< Previous
Next >
Nearby theorems |
||
Mirrors > Home > ILE Home > Th. List > rabeq0 | Unicode version |
Description: Condition for a restricted class abstraction to be empty. (Contributed by Jeff Madsen, 7-Jun-2010.) |
Ref | Expression |
---|---|
rabeq0 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | imnan 680 | . . 3 | |
2 | 1 | albii 1457 | . 2 |
3 | df-ral 2447 | . 2 | |
4 | sbn 1939 | . . . 4 | |
5 | 4 | albii 1457 | . . 3 |
6 | nfv 1515 | . . . 4 | |
7 | 6 | sb8 1843 | . . 3 |
8 | eq0 3425 | . . . 4 | |
9 | df-rab 2451 | . . . . . . . 8 | |
10 | 9 | eleq2i 2231 | . . . . . . 7 |
11 | df-clab 2151 | . . . . . . 7 | |
12 | 10, 11 | bitri 183 | . . . . . 6 |
13 | 12 | notbii 658 | . . . . 5 |
14 | 13 | albii 1457 | . . . 4 |
15 | 8, 14 | bitri 183 | . . 3 |
16 | 5, 7, 15 | 3bitr4ri 212 | . 2 |
17 | 2, 3, 16 | 3bitr4ri 212 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wi 4 wa 103 wb 104 wal 1340 wceq 1342 wsb 1749 wcel 2135 cab 2150 wral 2442 crab 2446 c0 3407 |
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-in1 604 ax-in2 605 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-fal 1348 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-rab 2451 df-v 2726 df-dif 3116 df-nul 3408 |
This theorem is referenced by: rabnc 3439 rabrsndc 3641 exmidsssnc 4179 ssfilem 6835 diffitest 6847 ssfirab 6893 ctssexmid 7108 exmidonfinlem 7143 iooidg 9839 icc0r 9856 fznlem 9970 ioo0 10189 ico0 10191 ioc0 10192 phiprmpw 12148 hashgcdeq 12165 unennn 12324 znnen 12325 |
Copyright terms: Public domain | W3C validator |