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Theorem bj-bd0el 12877
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 12876 . 2 BOUNDED 𝑦 = ∅
21bj-bdcel 12846 1 BOUNDED ∅ ∈ 𝑥
Colors of variables: wff set class
Syntax hints:  wcel 1463  c0 3331  BOUNDED wbd 12821
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 586  ax-in2 587  ax-io 681  ax-5 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097  ax-bd0 12822  ax-bdim 12823  ax-bdn 12826  ax-bdal 12827  ax-bdex 12828  ax-bdeq 12829
This theorem depends on definitions:  df-bi 116  df-tru 1317  df-fal 1320  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2245  df-ral 2396  df-rex 2397  df-v 2660  df-dif 3041  df-in 3045  df-ss 3052  df-nul 3332  df-bdc 12850
This theorem is referenced by:  bj-d0clsepcl  12934  bj-bdind  12939
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