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Mirrors > Home > ILE Home > Th. List > 0iin | Unicode version |
Description: An empty indexed intersection is the universal class. (Contributed by NM, 20-Oct-2005.) |
Ref | Expression |
---|---|
0iin |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-iin 3863 | . 2 | |
2 | vex 2724 | . . . 4 | |
3 | ral0 3505 | . . . 4 | |
4 | 2, 3 | 2th 173 | . . 3 |
5 | 4 | abbi2i 2279 | . 2 |
6 | 1, 5 | eqtr4i 2188 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 wcel 2135 cab 2150 wral 2442 cvv 2721 c0 3404 ciin 3861 |
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-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ral 2447 df-v 2723 df-dif 3113 df-nul 3405 df-iin 3863 |
This theorem is referenced by: riin0 3931 iin0r 4142 |
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