Theorem bdeli 16855

Description: Inference associated with bdel 16854. Its converse is bdelir 16856. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdeli.1	|- BOUNDED A

Assertion

Ref	Expression
bdeli	|- BOUNDED x e. A

Distinct variable group:   x, A

Proof of Theorem bdeli

Step	Hyp	Ref	Expression
1		bdeli.1	. 2 |- BOUNDED A
2		bdel 16854	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2209  BOUNDED wbd 16821  BOUNDED wbdc 16849

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1563

This theorem depends on definitions:  df-bi 117  df-bdc 16850

This theorem is referenced by:  bdph  16859  bdcrab  16861  bdnel  16863  bdccsb  16869  bdcdif  16870  bdcun  16871  bdcin  16872  bdss  16873  bdsnss  16882  bdciun  16887  bdciin  16888  bdinex1  16908  bj-inf2vnlem3  16981