Theorem bdeli 13881

Description: Inference associated with bdel 13880. Its converse is bdelir 13882. (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 13880	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2141  BOUNDED wbd 13847  BOUNDED wbdc 13875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1503

This theorem depends on definitions:  df-bi 116  df-bdc 13876

This theorem is referenced by:  bdph  13885  bdcrab  13887  bdnel  13889  bdccsb  13895  bdcdif  13896  bdcun  13897  bdcin  13898  bdss  13899  bdsnss  13908  bdciun  13913  bdciin  13914  bdinex1  13934  bj-uniex2  13951  bj-inf2vnlem3  14007