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Mirrors > Home > ILE Home > Th. List > vprc | Unicode version |
Description: The universal class is not a member of itself (and thus is not a set). Proposition 5.21 of [TakeutiZaring] p. 21; our proof, however, does not depend on the Axiom of Regularity. (Contributed by NM, 23-Aug-1993.) |
Ref | Expression |
---|---|
vprc |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nalset 3887 | . . 3 | |
2 | vex 2560 | . . . . . . 7 | |
3 | 2 | tbt 236 | . . . . . 6 |
4 | 3 | albii 1359 | . . . . 5 |
5 | dfcleq 2034 | . . . . 5 | |
6 | 4, 5 | bitr4i 176 | . . . 4 |
7 | 6 | exbii 1496 | . . 3 |
8 | 1, 7 | mtbi 595 | . 2 |
9 | isset 2561 | . 2 | |
10 | 8, 9 | mtbir 596 | 1 |
Colors of variables: wff set class |
Syntax hints: wn 3 wb 98 wal 1241 wceq 1243 wex 1381 wcel 1393 cvv 2557 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 99 ax-ia2 100 ax-ia3 101 ax-in1 544 ax-in2 545 ax-5 1336 ax-gen 1338 ax-ie1 1382 ax-ie2 1383 ax-8 1395 ax-4 1400 ax-13 1404 ax-14 1405 ax-17 1419 ax-i9 1423 ax-ial 1427 ax-ext 2022 ax-sep 3875 |
This theorem depends on definitions: df-bi 110 df-tru 1246 df-fal 1249 df-nf 1350 df-sb 1646 df-clab 2027 df-cleq 2033 df-clel 2036 df-v 2559 |
This theorem is referenced by: nvel 3889 vnex 3890 intexr 3904 intnexr 3905 snnex 4181 ruALT 4275 iprc 4600 |
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