Theorem bdeli 14534

Description: Inference associated with bdel 14533. Its converse is bdelir 14535. (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 14533	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2148  BOUNDED wbd 14500  BOUNDED wbdc 14528

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1510

This theorem depends on definitions:  df-bi 117  df-bdc 14529

This theorem is referenced by:  bdph  14538  bdcrab  14540  bdnel  14542  bdccsb  14548  bdcdif  14549  bdcun  14550  bdcin  14551  bdss  14552  bdsnss  14561  bdciun  14566  bdciin  14567  bdinex1  14587  bj-uniex2  14604  bj-inf2vnlem3  14660