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Theorem bj-bd0el 11189
Description: Boundedness of the formula "the empty set belongs to the setvar 𝑥". (Contributed by BJ, 30-Nov-2019.)
Assertion
Ref Expression
bj-bd0el BOUNDED ∅ ∈ 𝑥

Proof of Theorem bj-bd0el
Dummy variable 𝑦 is distinct from all other variables.
StepHypRef Expression
1 bdeq0 11188 . 2 BOUNDED 𝑦 = ∅
21bj-bdcel 11158 1 BOUNDED ∅ ∈ 𝑥
Colors of variables: wff set class
Syntax hints:  wcel 1436  c0 3275  BOUNDED wbd 11133
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-in1 577  ax-in2 578  ax-io 663  ax-5 1379  ax-7 1380  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-8 1438  ax-10 1439  ax-11 1440  ax-i12 1441  ax-bndl 1442  ax-4 1443  ax-17 1462  ax-i9 1466  ax-ial 1470  ax-i5r 1471  ax-ext 2067  ax-bd0 11134  ax-bdim 11135  ax-bdn 11138  ax-bdal 11139  ax-bdex 11140  ax-bdeq 11141
This theorem depends on definitions:  df-bi 115  df-tru 1290  df-fal 1293  df-nf 1393  df-sb 1690  df-clab 2072  df-cleq 2078  df-clel 2081  df-nfc 2214  df-ral 2360  df-rex 2361  df-v 2617  df-dif 2990  df-in 2994  df-ss 3001  df-nul 3276  df-bdc 11162
This theorem is referenced by:  bj-d0clsepcl  11250  bj-bdind  11255
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