Theorem bdelir 10638

Description: Inference associated with df-bdc 10632. Its converse is bdeli 10637. (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 10632	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		bdelir.1	. 2 |- BOUNDED x e. A
3	1, 2	mpgbir 1382	1 |- BOUNDED A

Syntax hints:   e. wcel 1433  BOUNDED wbd 10603  BOUNDED wbdc 10631

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 1378

This theorem depends on definitions:  df-bi 115  df-bdc 10632

This theorem is referenced by:  bdcv  10639  bdcab  10640  bdcvv  10648  bdcnul  10656  bdop  10666