Theorem bdeli 16167

Description: Inference associated with bdel 16166. Its converse is bdelir 16168. (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 16166	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2200  BOUNDED wbd 16133  BOUNDED wbdc 16161

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1556

This theorem depends on definitions:  df-bi 117  df-bdc 16162

This theorem is referenced by:  bdph  16171  bdcrab  16173  bdnel  16175  bdccsb  16181  bdcdif  16182  bdcun  16183  bdcin  16184  bdss  16185  bdsnss  16194  bdciun  16199  bdciin  16200  bdinex1  16220  bj-uniex2  16237  bj-inf2vnlem3  16293