Theorem bdeli 17094

Description: Inference associated with bdel 17093. Its converse is bdelir 17095. (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 17093	. 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 17060  BOUNDED wbdc 17088

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 17089

This theorem is used by:  bdph  17098  bdcrab  17100  bdnel  17102  bdccsb  17108  bdcdif  17109  bdcun  17110  bdcin  17111  bdss  17112  bdsnss  17121  bdciun  17126  bdciin  17127  bdinex1  17147  bj-inf2vnlem3  17220