Theorem bdeli 15744

Description: Inference associated with bdel 15743. Its converse is bdelir 15745. (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 15743	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2175  BOUNDED wbd 15710  BOUNDED wbdc 15738

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1532

This theorem depends on definitions:  df-bi 117  df-bdc 15739

This theorem is referenced by:  bdph  15748  bdcrab  15750  bdnel  15752  bdccsb  15758  bdcdif  15759  bdcun  15760  bdcin  15761  bdss  15762  bdsnss  15771  bdciun  15776  bdciin  15777  bdinex1  15797  bj-uniex2  15814  bj-inf2vnlem3  15870