Theorem bj-bdsucel 15818

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 15817	. 2 |- BOUNDED z = suc x
2	1	bj-bdcel 15773	1 |- BOUNDED suc x e. y

Syntax hints:   e. wcel 2176   suc csuc 4412  BOUNDED wbd 15748

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 711  ax-5 1470  ax-7 1471  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-8 1527  ax-10 1528  ax-11 1529  ax-i12 1530  ax-bndl 1532  ax-4 1533  ax-17 1549  ax-i9 1553  ax-ial 1557  ax-i5r 1558  ax-ext 2187  ax-bd0 15749  ax-bdan 15751  ax-bdor 15752  ax-bdal 15754  ax-bdex 15755  ax-bdeq 15756  ax-bdel 15757  ax-bdsb 15758

This theorem depends on definitions:  df-bi 117  df-tru 1376  df-nf 1484  df-sb 1786  df-clab 2192  df-cleq 2198  df-clel 2201  df-nfc 2337  df-ral 2489  df-rex 2490  df-v 2774  df-un 3170  df-in 3172  df-ss 3179  df-sn 3639  df-suc 4418  df-bdc 15777

This theorem is referenced by:  bj-bdind  15866