Theorem bdelir 13689

Description: Inference associated with df-bdc 13683. Its converse is bdeli 13688. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdelir.1	|- BOUNDED x e. A

Assertion

Ref	Expression
bdelir	|- BOUNDED A

Distinct variable group:   x, A

Proof of Theorem bdelir

Step	Hyp	Ref	Expression
1		df-bdc 13683	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		bdelir.1	. 2 |- BOUNDED x e. A
3	1, 2	mpgbir 1441	1 |- BOUNDED A

Syntax hints:   e. wcel 2136  BOUNDED wbd 13654  BOUNDED wbdc 13682

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-gen 1437

This theorem depends on definitions:  df-bi 116  df-bdc 13683

This theorem is referenced by:  bdcv  13690  bdcab  13691  bdcvv  13699  bdcnul  13707  bdop  13717