Theorem bdel 9965

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 9961	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		sp 1401	. 2 |- ( A. xBOUNDED x e. A -> BOUNDED x e. A )
3	1, 2	sylbi 114	1 |- (BOUNDED A -> BOUNDED x e. A )

Syntax hints:   -> wi 4   A.wal 1241   e. wcel 1393  BOUNDED wbd 9932  BOUNDED wbdc 9960

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-4 1400

This theorem depends on definitions:  df-bi 110  df-bdc 9961

This theorem is referenced by:  bdeli  9966