Theorem bdel 16871

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 16867	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		sp 1564	. 2 |- ( A. xBOUNDED x e. A -> BOUNDED x e. A )
3	1, 2	sylbi 121	1 |- (BOUNDED A -> BOUNDED x e. A )

This proof depends on syntax axioms:   -> wi 4   A.wal 1400   e. wcel 2209  BOUNDED wbd 16838  BOUNDED wbdc 16866

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1563

This proof depends on definitions:  df-bi 117  df-bdc 16867

This theorem is used by:  bdeli  16872