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Mirrors > Home > ILE Home > Th. List > ruv | Unicode version |
Description: The Russell class is equal to the universe . Exercise 5 of [TakeutiZaring] p. 22. (Contributed by Alan Sare, 4-Oct-2008.) |
Ref | Expression |
---|---|
ruv |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-v 2723 | . 2 | |
2 | equid 1688 | . . . 4 | |
3 | elirrv 4519 | . . . . 5 | |
4 | 3 | nelir 2432 | . . . 4 |
5 | 2, 4 | 2th 173 | . . 3 |
6 | 5 | abbii 2280 | . 2 |
7 | 1, 6 | eqtr2i 2186 | 1 |
Colors of variables: wff set class |
Syntax hints: wceq 1342 cab 2150 wnel 2429 cvv 2721 |
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 ax-setind 4508 |
This theorem depends on definitions: df-bi 116 df-3an 969 df-tru 1345 df-nf 1448 df-sb 1750 df-clab 2151 df-cleq 2157 df-clel 2160 df-nfc 2295 df-ne 2335 df-nel 2430 df-ral 2447 df-v 2723 df-dif 3113 df-sn 3576 |
This theorem is referenced by: ruALT 4522 |
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