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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 3786 | . 2 | |
2 | vex 2663 | . . . 4 | |
3 | ral0 3434 | . . . 4 | |
4 | 2, 3 | 2th 173 | . . 3 |
5 | 4 | abbi2i 2232 | . 2 |
6 | 1, 5 | eqtr4i 2141 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1316 wcel 1465 cab 2103 wral 2393 cvv 2660 c0 3333 ciin 3784 |
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 588 ax-in2 589 ax-io 683 ax-5 1408 ax-7 1409 ax-gen 1410 ax-ie1 1454 ax-ie2 1455 ax-8 1467 ax-10 1468 ax-11 1469 ax-i12 1470 ax-bndl 1471 ax-4 1472 ax-17 1491 ax-i9 1495 ax-ial 1499 ax-i5r 1500 ax-ext 2099 |
This theorem depends on definitions: df-bi 116 df-tru 1319 df-nf 1422 df-sb 1721 df-clab 2104 df-cleq 2110 df-clel 2113 df-nfc 2247 df-ral 2398 df-v 2662 df-dif 3043 df-nul 3334 df-iin 3786 |
This theorem is referenced by: riin0 3854 iin0r 4063 |
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