Theorem bj-bdsucel 16477

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 16476	. 2 |- BOUNDED z = suc x
2	1	bj-bdcel 16432	1 |- BOUNDED suc x e. y

Syntax hints:   e. wcel 2202   suc csuc 4462  BOUNDED wbd 16407

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 716  ax-5 1495  ax-7 1496  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-8 1552  ax-10 1553  ax-11 1554  ax-i12 1555  ax-bndl 1557  ax-4 1558  ax-17 1574  ax-i9 1578  ax-ial 1582  ax-i5r 1583  ax-ext 2213  ax-bd0 16408  ax-bdan 16410  ax-bdor 16411  ax-bdal 16413  ax-bdex 16414  ax-bdeq 16415  ax-bdel 16416  ax-bdsb 16417

This theorem depends on definitions:  df-bi 117  df-tru 1400  df-nf 1509  df-sb 1811  df-clab 2218  df-cleq 2224  df-clel 2227  df-nfc 2363  df-ral 2515  df-rex 2516  df-v 2804  df-un 3204  df-in 3206  df-ss 3213  df-sn 3675  df-suc 4468  df-bdc 16436

This theorem is referenced by:  bj-bdind  16525