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Theorem bj-bd0el 10944
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 10943 . 2 BOUNDED 𝑦 = ∅
21bj-bdcel 10913 1 BOUNDED ∅ ∈ 𝑥
Colors of variables: wff set class
Syntax hints:  wcel 1434  c0 3267  BOUNDED wbd 10888
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 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065  ax-bd0 10889  ax-bdim 10890  ax-bdn 10893  ax-bdal 10894  ax-bdex 10895  ax-bdeq 10896
This theorem depends on definitions:  df-bi 115  df-tru 1288  df-fal 1291  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-ral 2358  df-rex 2359  df-v 2612  df-dif 2984  df-in 2988  df-ss 2995  df-nul 3268  df-bdc 10917
This theorem is referenced by:  bj-d0clsepcl  11005  bj-bdind  11010
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