Theorem bdeli 16872

Description: Inference associated with bdel 16871. Its converse is bdelir 16873. (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 16871	. 2 |- (BOUNDED A -> BOUNDED x e. A )
3	1, 2	ax-mp 5	1 |- BOUNDED x e. A

This proof depends on syntax axioms:   e. wcel 2209  BOUNDED wbd 16838  BOUNDED wbdc 16866

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1563

This proof depends on definitions:  df-bi 117  df-bdc 16867

This theorem is used by:  bdph  16876  bdcrab  16878  bdnel  16880  bdccsb  16886  bdcdif  16887  bdcun  16888  bdcin  16889  bdss  16890  bdsnss  16899  bdciun  16904  bdciin  16905  bdinex1  16925  bj-inf2vnlem3  16998