Theorem bdeli 17006

Description: Inference associated with bdel 17005. Its converse is bdelir 17007. (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 17005	. 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 16972  BOUNDED wbdc 17000

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 17001

This theorem is used by:  bdph  17010  bdcrab  17012  bdnel  17014  bdccsb  17020  bdcdif  17021  bdcun  17022  bdcin  17023  bdss  17024  bdsnss  17033  bdciun  17038  bdciin  17039  bdinex1  17059  bj-inf2vnlem3  17132