Theorem bdeli 16545

Description: Inference associated with bdel 16544. Its converse is bdelir 16546. (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 16544	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2202  BOUNDED wbd 16511  BOUNDED wbdc 16539

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1559

This theorem depends on definitions:  df-bi 117  df-bdc 16540

This theorem is referenced by:  bdph  16549  bdcrab  16551  bdnel  16553  bdccsb  16559  bdcdif  16560  bdcun  16561  bdcin  16562  bdss  16563  bdsnss  16572  bdciun  16577  bdciin  16578  bdinex1  16598  bj-uniex2  16615  bj-inf2vnlem3  16671