Theorem bdeli 10637

Description: Inference associated with bdel 10636. Its converse is bdelir 10638. (Contributed by BJ, 3-Oct-2019.)

Hypothesis

Ref	Expression
bdeli.1	⊢ BOUNDED 𝐴

Assertion

Ref	Expression
bdeli	⊢ BOUNDED 𝑥 ∈ 𝐴

Distinct variable group:   𝑥,𝐴

Proof of Theorem bdeli

Step	Hyp	Ref	Expression
1		bdeli.1	. 2 ⊢ BOUNDED 𝐴
2		bdel 10636	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 7	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 1433  BOUNDED wbd 10603  BOUNDED wbdc 10631

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-4 1440

This theorem depends on definitions:  df-bi 115  df-bdc 10632

This theorem is referenced by:  bdph  10641  bdcrab  10643  bdnel  10645  bdccsb  10651  bdcdif  10652  bdcun  10653  bdcin  10654  bdss  10655  bdsnss  10664  bdciun  10669  bdciin  10670  bdinex1  10690  bj-uniex2  10707  bj-inf2vnlem3  10767