Theorem bdelir 13882

Description: Inference associated with df-bdc 13876. Its converse is bdeli 13881. (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 13876	. 2 |- (BOUNDED A <-> A. xBOUNDED x e. A )
2		bdelir.1	. 2 |- BOUNDED x e. A
3	1, 2	mpgbir 1446	1 |- BOUNDED A

Syntax hints:   e. wcel 2141  BOUNDED wbd 13847  BOUNDED wbdc 13875

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 1442

This theorem depends on definitions:  df-bi 116  df-bdc 13876

This theorem is referenced by:  bdcv  13883  bdcab  13884  bdcvv  13892  bdcnul  13900  bdop  13910