Theorem bdeli 16742

Description: Inference associated with bdel 16741. Its converse is bdelir 16743. (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 16741	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2205  BOUNDED wbd 16708  BOUNDED wbdc 16736

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1559

This theorem depends on definitions:  df-bi 117  df-bdc 16737

This theorem is referenced by:  bdph  16746  bdcrab  16748  bdnel  16750  bdccsb  16756  bdcdif  16757  bdcun  16758  bdcin  16759  bdss  16760  bdsnss  16769  bdciun  16774  bdciin  16775  bdinex1  16795  bj-uniex2  16812  bj-inf2vnlem3  16868