Theorem bdeli 16786

Description: Inference associated with bdel 16785. Its converse is bdelir 16787. (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 16785	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2209  BOUNDED wbd 16752  BOUNDED wbdc 16780

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1563

This theorem depends on definitions:  df-bi 117  df-bdc 16781

This theorem is referenced by:  bdph  16790  bdcrab  16792  bdnel  16794  bdccsb  16800  bdcdif  16801  bdcun  16802  bdcin  16803  bdss  16804  bdsnss  16813  bdciun  16818  bdciin  16819  bdinex1  16839  bj-inf2vnlem3  16912