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Theorem bdvsn 9994
 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 9990 . . . 4 BOUNDED
21bdss 9984 . . 3 BOUNDED
3 bdcv 9968 . . . 4 BOUNDED
43bdsnss 9993 . . 3 BOUNDED
52, 4ax-bdan 9935 . 2 BOUNDED
6 eqss 2960 . 2
75, 6bd0r 9945 1 BOUNDED
 Colors of variables: wff set class Syntax hints:   wa 97   wceq 1243   wss 2917  csn 3375  BOUNDED wbd 9932 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-bndl 1399  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022  ax-bd0 9933  ax-bdan 9935  ax-bdal 9938  ax-bdeq 9940  ax-bdel 9941  ax-bdsb 9942 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033  df-clel 2036  df-nfc 2167  df-ral 2311  df-v 2559  df-in 2924  df-ss 2931  df-sn 3381  df-bdc 9961 This theorem is referenced by:  bdop  9995
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