Theorem bdeli 15492

Description: Inference associated with bdel 15491. Its converse is bdelir 15493. (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 15491	. 2 ⊢ (BOUNDED 𝐴 → BOUNDED 𝑥 ∈ 𝐴)
3	1, 2	ax-mp 5	1 ⊢ BOUNDED 𝑥 ∈ 𝐴

Syntax hints:   ∈ wcel 2167  BOUNDED wbd 15458  BOUNDED wbdc 15486

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-4 1524

This theorem depends on definitions:  df-bi 117  df-bdc 15487

This theorem is referenced by:  bdph  15496  bdcrab  15498  bdnel  15500  bdccsb  15506  bdcdif  15507  bdcun  15508  bdcin  15509  bdss  15510  bdsnss  15519  bdciun  15524  bdciin  15525  bdinex1  15545  bj-uniex2  15562  bj-inf2vnlem3  15618