Theorem bdeli 15981

Description: Inference associated with bdel 15980. Its converse is bdelir 15982. (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 15980	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2178  BOUNDED wbd 15947  BOUNDED wbdc 15975

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1534

This theorem depends on definitions:  df-bi 117  df-bdc 15976

This theorem is referenced by:  bdph  15985  bdcrab  15987  bdnel  15989  bdccsb  15995  bdcdif  15996  bdcun  15997  bdcin  15998  bdss  15999  bdsnss  16008  bdciun  16013  bdciin  16014  bdinex1  16034  bj-uniex2  16051  bj-inf2vnlem3  16107