Theorem bdeli 15576

Description: Inference associated with bdel 15575. Its converse is bdelir 15577. (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 15575	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2167  BOUNDED wbd 15542  BOUNDED wbdc 15570

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1524

This theorem depends on definitions:  df-bi 117  df-bdc 15571

This theorem is referenced by:  bdph  15580  bdcrab  15582  bdnel  15584  bdccsb  15590  bdcdif  15591  bdcun  15592  bdcin  15593  bdss  15594  bdsnss  15603  bdciun  15608  bdciin  15609  bdinex1  15629  bj-uniex2  15646  bj-inf2vnlem3  15702