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Theorem bj-bd0el 14847
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  (/)  e.  x

Proof of Theorem bj-bd0el
Dummy variable  y is distinct from all other variables.
StepHypRef Expression
1 bdeq0 14846 . 2  |- BOUNDED  y  =  (/)
21bj-bdcel 14816 1  |- BOUNDED  (/)  e.  x
Colors of variables: wff set class
Syntax hints:    e. wcel 2158   (/)c0 3434  BOUNDED wbd 14791
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 1457  ax-7 1458  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-8 1514  ax-10 1515  ax-11 1516  ax-i12 1517  ax-bndl 1519  ax-4 1520  ax-17 1536  ax-i9 1540  ax-ial 1544  ax-i5r 1545  ax-ext 2169  ax-bd0 14792  ax-bdim 14793  ax-bdn 14796  ax-bdal 14797  ax-bdex 14798  ax-bdeq 14799
This theorem depends on definitions:  df-bi 117  df-tru 1366  df-fal 1369  df-nf 1471  df-sb 1773  df-clab 2174  df-cleq 2180  df-clel 2183  df-nfc 2318  df-ral 2470  df-rex 2471  df-v 2751  df-dif 3143  df-in 3147  df-ss 3154  df-nul 3435  df-bdc 14820
This theorem is referenced by:  bj-d0clsepcl  14904  bj-bdind  14909
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