Theorem bdeli 15600

Description: Inference associated with bdel 15599. Its converse is bdelir 15601. (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 15599	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2167  BOUNDED wbd 15566  BOUNDED wbdc 15594

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 15595

This theorem is referenced by:  bdph  15604  bdcrab  15606  bdnel  15608  bdccsb  15614  bdcdif  15615  bdcun  15616  bdcin  15617  bdss  15618  bdsnss  15627  bdciun  15632  bdciin  15633  bdinex1  15653  bj-uniex2  15670  bj-inf2vnlem3  15726