Theorem bdeli 16884

Description: Inference associated with bdel 16883. Its converse is bdelir 16885. (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 16883	. 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 16850  BOUNDED wbdc 16878

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 16879

This theorem is used by:  bdph  16888  bdcrab  16890  bdnel  16892  bdccsb  16898  bdcdif  16899  bdcun  16900  bdcin  16901  bdss  16902  bdsnss  16911  bdciun  16916  bdciin  16917  bdinex1  16937  bj-inf2vnlem3  17010