Theorem bdeli 17038

Description: Inference associated with bdel 17037. Its converse is bdelir 17039. (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 17037	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

This proof depends on syntax axioms:   ∈ wcel 2209  BOUNDED wbd 17004  BOUNDED wbdc 17032

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1563

This proof depends on definitions:  df-bi 117  df-bdc 17033

This theorem is used by:  bdph  17042  bdcrab  17044  bdnel  17046  bdccsb  17052  bdcdif  17053  bdcun  17054  bdcin  17055  bdss  17056  bdsnss  17065  bdciun  17070  bdciin  17071  bdinex1  17091  bj-inf2vnlem3  17164