Theorem bdeli 15338

Description: Inference associated with bdel 15337. Its converse is bdelir 15339. (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 15337	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2164  BOUNDED wbd 15304  BOUNDED wbdc 15332

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 15333

This theorem is referenced by:  bdph  15342  bdcrab  15344  bdnel  15346  bdccsb  15352  bdcdif  15353  bdcun  15354  bdcin  15355  bdss  15356  bdsnss  15365  bdciun  15370  bdciin  15371  bdinex1  15391  bj-uniex2  15408  bj-inf2vnlem3  15464