Theorem bdeli 13044

Description: Inference associated with bdel 13043. Its converse is bdelir 13045. (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 13043	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 1480  BOUNDED wbd 13010  BOUNDED wbdc 13038

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1487

This theorem depends on definitions:  df-bi 116  df-bdc 13039

This theorem is referenced by:  bdph  13048  bdcrab  13050  bdnel  13052  bdccsb  13058  bdcdif  13059  bdcun  13060  bdcin  13061  bdss  13062  bdsnss  13071  bdciun  13076  bdciin  13077  bdinex1  13097  bj-uniex2  13114  bj-inf2vnlem3  13170