Theorem bdeli 14637

Description: Inference associated with bdel 14636. Its converse is bdelir 14638. (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 14636	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2148  BOUNDED wbd 14603  BOUNDED wbdc 14631

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1510

This theorem depends on definitions:  df-bi 117  df-bdc 14632

This theorem is referenced by:  bdph  14641  bdcrab  14643  bdnel  14645  bdccsb  14651  bdcdif  14652  bdcun  14653  bdcin  14654  bdss  14655  bdsnss  14664  bdciun  14669  bdciin  14670  bdinex1  14690  bj-uniex2  14707  bj-inf2vnlem3  14763