Theorem bdeli 15782

Description: Inference associated with bdel 15781. Its converse is bdelir 15783. (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 15781	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2176  BOUNDED wbd 15748  BOUNDED wbdc 15776

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1533

This theorem depends on definitions:  df-bi 117  df-bdc 15777

This theorem is referenced by:  bdph  15786  bdcrab  15788  bdnel  15790  bdccsb  15796  bdcdif  15797  bdcun  15798  bdcin  15799  bdss  15800  bdsnss  15809  bdciun  15814  bdciin  15815  bdinex1  15835  bj-uniex2  15852  bj-inf2vnlem3  15908