Theorem bj-bd0el 16638

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.

Step	Hyp	Ref	Expression
1		bdeq0 16637	. 2 ⊢ BOUNDED 𝑦 = ∅
2	1	bj-bdcel 16607	1 ⊢ BOUNDED ∅ ∈ 𝑥

Syntax hints:   ∈ wcel 2203  ∅c0 3508  BOUNDED wbd 16582

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 619  ax-in2 620  ax-io 717  ax-5 1496  ax-7 1497  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-8 1553  ax-10 1554  ax-11 1555  ax-i12 1556  ax-bndl 1558  ax-4 1559  ax-17 1575  ax-i9 1579  ax-ial 1583  ax-i5r 1584  ax-ext 2214  ax-bd0 16583  ax-bdim 16584  ax-bdn 16587  ax-bdal 16588  ax-bdex 16589  ax-bdeq 16590

This theorem depends on definitions:  df-bi 117  df-tru 1401  df-fal 1404  df-nf 1510  df-sb 1812  df-clab 2219  df-cleq 2225  df-clel 2228  df-nfc 2373  df-ral 2525  df-rex 2526  df-v 2815  df-dif 3213  df-in 3217  df-ss 3224  df-nul 3509  df-bdc 16611

This theorem is referenced by:  bj-d0clsepcl  16695  bj-bdind  16700