Theorem bdcv 17045

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 17018	. 2 ⊢ BOUNDED 𝑦 ∈ 𝑥
2	1	bdelir 17044	1 ⊢ BOUNDED 𝑥

This proof depends on syntax axioms:  BOUNDED wbdc 17037

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 17018

This proof depends on definitions:  df-bi 117  df-bdc 17038

This theorem is used by:  bdvsn  17071  bdcsuc  17077  bdeqsuc  17078  bj-inex  17104  bj-nntrans  17148  bj-omtrans  17153  bj-inf2vn  17171  bj-omex2  17174  bj-nn0sucALT  17175