Theorem bdelir 11382

Description: Inference associated with df-bdc 11376. Its converse is bdeli 11381. (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 11376	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		bdelir.1	. 2 |- BOUNDED x e. A
3	1, 2	mpgbir 1387	1 |- BOUNDED A

Syntax hints:   e. wcel 1438  BOUNDED wbd 11347  BOUNDED wbdc 11375

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 1383

This theorem depends on definitions:  df-bi 115  df-bdc 11376

This theorem is referenced by:  bdcv  11383  bdcab  11384  bdcvv  11392  bdcnul  11400  bdop  11410