Theorem bdeli 16616

Description: Inference associated with bdel 16615. Its converse is bdelir 16617. (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 16615	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2203  BOUNDED wbd 16582  BOUNDED wbdc 16610

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 16611

This theorem is referenced by:  bdph  16620  bdcrab  16622  bdnel  16624  bdccsb  16630  bdcdif  16631  bdcun  16632  bdcin  16633  bdss  16634  bdsnss  16643  bdciun  16648  bdciin  16649  bdinex1  16669  bj-uniex2  16686  bj-inf2vnlem3  16742