Theorem bdeli 15408

Description: Inference associated with bdel 15407. Its converse is bdelir 15409. (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 15407	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2164  BOUNDED wbd 15374  BOUNDED wbdc 15402

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1521

This theorem depends on definitions:  df-bi 117  df-bdc 15403

This theorem is referenced by:  bdph  15412  bdcrab  15414  bdnel  15416  bdccsb  15422  bdcdif  15423  bdcun  15424  bdcin  15425  bdss  15426  bdsnss  15435  bdciun  15440  bdciin  15441  bdinex1  15461  bj-uniex2  15478  bj-inf2vnlem3  15534