Theorem bdeli 13728

Description: Inference associated with bdel 13727. Its converse is bdelir 13729. (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 13727	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2136  BOUNDED wbd 13694  BOUNDED wbdc 13722

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1498

This theorem depends on definitions:  df-bi 116  df-bdc 13723

This theorem is referenced by:  bdph  13732  bdcrab  13734  bdnel  13736  bdccsb  13742  bdcdif  13743  bdcun  13744  bdcin  13745  bdss  13746  bdsnss  13755  bdciun  13760  bdciin  13761  bdinex1  13781  bj-uniex2  13798  bj-inf2vnlem3  13854