Theorem bdeli 15819

Description: Inference associated with bdel 15818. Its converse is bdelir 15820. (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 15818	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

Syntax hints:   e. wcel 2176  BOUNDED wbd 15785  BOUNDED wbdc 15813

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1533

This theorem depends on definitions:  df-bi 117  df-bdc 15814

This theorem is referenced by:  bdph  15823  bdcrab  15825  bdnel  15827  bdccsb  15833  bdcdif  15834  bdcun  15835  bdcin  15836  bdss  15837  bdsnss  15846  bdciun  15851  bdciin  15852  bdinex1  15872  bj-uniex2  15889  bj-inf2vnlem3  15945