Theorem bj-bdsucel 16245

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 16244	. 2 |- BOUNDED z = suc x
2	1	bj-bdcel 16200	1 |- BOUNDED suc x e. y

Syntax hints:   e. wcel 2200   suc csuc 4456  BOUNDED wbd 16175

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 714  ax-5 1493  ax-7 1494  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-8 1550  ax-10 1551  ax-11 1552  ax-i12 1553  ax-bndl 1555  ax-4 1556  ax-17 1572  ax-i9 1576  ax-ial 1580  ax-i5r 1581  ax-ext 2211  ax-bd0 16176  ax-bdan 16178  ax-bdor 16179  ax-bdal 16181  ax-bdex 16182  ax-bdeq 16183  ax-bdel 16184  ax-bdsb 16185

This theorem depends on definitions:  df-bi 117  df-tru 1398  df-nf 1507  df-sb 1809  df-clab 2216  df-cleq 2222  df-clel 2225  df-nfc 2361  df-ral 2513  df-rex 2514  df-v 2801  df-un 3201  df-in 3203  df-ss 3210  df-sn 3672  df-suc 4462  df-bdc 16204

This theorem is referenced by:  bj-bdind  16293