Theorem bdeli 16441

Description: Inference associated with bdel 16440. Its converse is bdelir 16442. (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 16440	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2202  BOUNDED wbd 16407  BOUNDED wbdc 16435

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1558

This theorem depends on definitions:  df-bi 117  df-bdc 16436

This theorem is referenced by:  bdph  16445  bdcrab  16447  bdnel  16449  bdccsb  16455  bdcdif  16456  bdcun  16457  bdcin  16458  bdss  16459  bdsnss  16468  bdciun  16473  bdciin  16474  bdinex1  16494  bj-uniex2  16511  bj-inf2vnlem3  16567