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Theorem bj-bd0el 15073
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 15072 . 2 BOUNDED 𝑦 = ∅
21bj-bdcel 15042 1 BOUNDED ∅ ∈ 𝑥
Colors of variables: wff set class
Syntax hints:  wcel 2160  c0 3437  BOUNDED wbd 15017
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171  ax-bd0 15018  ax-bdim 15019  ax-bdn 15022  ax-bdal 15023  ax-bdex 15024  ax-bdeq 15025
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-fal 1370  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ral 2473  df-rex 2474  df-v 2754  df-dif 3146  df-in 3150  df-ss 3157  df-nul 3438  df-bdc 15046
This theorem is referenced by:  bj-d0clsepcl  15130  bj-bdind  15135
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