Theorem bdel 13737

Description: The belonging of a setvar in a bounded class is a bounded formula. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdel	|- (BOUNDED A -> BOUNDED x e. A )

Distinct variable group:   x, A

Proof of Theorem bdel

Step	Hyp	Ref	Expression
1		df-bdc 13733	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		sp 1499	. 2 |- ( A. xBOUNDED x e. A -> BOUNDED x e. A )
3	1, 2	sylbi 120	1 |- (BOUNDED A -> BOUNDED x e. A )

Syntax hints:   -> wi 4   A.wal 1341   e. wcel 2136  BOUNDED wbd 13704  BOUNDED wbdc 13732

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1498

This theorem depends on definitions:  df-bi 116  df-bdc 13733

This theorem is referenced by:  bdeli  13738