Theorem bdeli 13381

Description: Inference associated with bdel 13380. Its converse is bdelir 13382. (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 13380	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2128  BOUNDED wbd 13347  BOUNDED wbdc 13375

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-4 1490

This theorem depends on definitions:  df-bi 116  df-bdc 13376

This theorem is referenced by:  bdph  13385  bdcrab  13387  bdnel  13389  bdccsb  13395  bdcdif  13396  bdcun  13397  bdcin  13398  bdss  13399  bdsnss  13408  bdciun  13413  bdciin  13414  bdinex1  13434  bj-uniex2  13451  bj-inf2vnlem3  13507