Theorem bdelir 11095

Description: Inference associated with df-bdc 11089. Its converse is bdeli 11094. (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 11089	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		bdelir.1	. 2 |- BOUNDED x e. A
3	1, 2	mpgbir 1385	1 |- BOUNDED A

Syntax hints:   e. wcel 1436  BOUNDED wbd 11060  BOUNDED wbdc 11088

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-gen 1381

This theorem depends on definitions:  df-bi 115  df-bdc 11089

This theorem is referenced by:  bdcv  11096  bdcab  11097  bdcvv  11105  bdcnul  11113  bdop  11123