Theorem bdcv 17112

Description: A setvar is a bounded class. (Contributed by BJ, 3-Oct-2019.)

Assertion

Ref	Expression
bdcv	⊢ BOUNDED 𝑥

Proof of Theorem bdcv

Dummy variable 𝑦 is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax-bdel 17085	. 2 ⊢ BOUNDED 𝑦 ∈ 𝑥
2	1	bdelir 17111	1 ⊢ BOUNDED 𝑥

This proof depends on syntax axioms:  BOUNDED wbdc 17104

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-gen 1502  ax-bdel 17085

This proof depends on definitions:  df-bi 117  df-bdc 17105

This theorem is used by:  bdvsn  17138  bdcsuc  17144  bdeqsuc  17145  bj-inex  17171  bj-nntrans  17215  bj-omtrans  17220  bj-inf2vn  17238  bj-omex2  17241  bj-nn0sucALT  17242