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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 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | vnex 4067 |
. 2
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2 | isset 2695 |
. 2
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3 | 1, 2 | mtbir 661 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() |
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-5 1424 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-4 1488 ax-13 1492 ax-14 1493 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-ext 2122 ax-sep 4054 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-fal 1338 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-v 2691 |
This theorem is referenced by: nvel 4069 intexr 4083 intnexr 4084 abnex 4376 snnex 4377 ruALT 4474 dcextest 4503 iprc 4815 snexxph 6846 elfi2 6868 fi0 6871 |
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