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Theorem bdvsn 9329
Description: Equality of a setvar with a singleton of a setvar is a bounded formula. (Contributed by BJ, 16-Oct-2019.)
Assertion
Ref Expression
bdvsn BOUNDED  { }
Distinct variable group:   ,

Proof of Theorem bdvsn
StepHypRef Expression
1 bdcsn 9325 . . . 4 BOUNDED  { }
21bdss 9319 . . 3 BOUNDED  C_  { }
3 bdcv 9303 . . . 4 BOUNDED
43bdsnss 9328 . . 3 BOUNDED  { }  C_
52, 4ax-bdan 9270 . 2 BOUNDED  C_  { }  { }  C_
6 eqss 2954 . 2  { }  C_  { }  { }  C_
75, 6bd0r 9280 1 BOUNDED  { }
Colors of variables: wff set class
Syntax hints:   wa 97   wceq 1242    C_ wss 2911   {csn 3367  BOUNDED wbd 9267
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-5 1333  ax-7 1334  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-11 1394  ax-4 1397  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-i5r 1425  ax-ext 2019  ax-bd0 9268  ax-bdan 9270  ax-bdal 9273  ax-bdeq 9275  ax-bdel 9276  ax-bdsb 9277
This theorem depends on definitions:  df-bi 110  df-nf 1347  df-sb 1643  df-clab 2024  df-cleq 2030  df-clel 2033  df-ral 2305  df-v 2553  df-in 2918  df-ss 2925  df-sn 3373  df-bdc 9296
This theorem is referenced by:  bdop  9330
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