Theorem bj-bdsucel 15780

Description: Boundedness of the formula "the successor of the setvar x belongs to the setvar y". (Contributed by BJ, 30-Nov-2019.)

Assertion

Ref	Expression
bj-bdsucel	|- BOUNDED suc x e. y

Proof of Theorem bj-bdsucel

Dummy variable z is distinct from all other variables.

Step	Hyp	Ref	Expression
1		bdeqsuc 15779	. 2 |- BOUNDED z = suc x
2	1	bj-bdcel 15735	1 |- BOUNDED suc x e. y

Syntax hints:   e. wcel 2175   suc csuc 4411  BOUNDED wbd 15710

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-io 710  ax-5 1469  ax-7 1470  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-8 1526  ax-10 1527  ax-11 1528  ax-i12 1529  ax-bndl 1531  ax-4 1532  ax-17 1548  ax-i9 1552  ax-ial 1556  ax-i5r 1557  ax-ext 2186  ax-bd0 15711  ax-bdan 15713  ax-bdor 15714  ax-bdal 15716  ax-bdex 15717  ax-bdeq 15718  ax-bdel 15719  ax-bdsb 15720

This theorem depends on definitions:  df-bi 117  df-tru 1375  df-nf 1483  df-sb 1785  df-clab 2191  df-cleq 2197  df-clel 2200  df-nfc 2336  df-ral 2488  df-rex 2489  df-v 2773  df-un 3169  df-in 3171  df-ss 3178  df-sn 3638  df-suc 4417  df-bdc 15739

This theorem is referenced by:  bj-bdind  15828