Theorem bdcsn 14504

Description: The singleton of a setvar is bounded. (Contributed by BJ, 16-Oct-2019.)

Assertion

Ref	Expression
bdcsn	|- BOUNDED { x }

Proof of Theorem bdcsn

Dummy variable y is distinct from all other variables.

Step	Hyp	Ref	Expression
1		ax-bdeq 14454	. . 3 |- BOUNDED y = x
2	1	bdcab 14483	. 2 |- BOUNDED { y | y = x }
3		df-sn 3598	. 2 |- { x } = { y | y = x }
4	2, 3	bdceqir 14478	1 |- BOUNDED { x }

Syntax hints:   {cab 2163   {csn 3592  BOUNDED wbdc 14474

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14447  ax-bdeq 14454  ax-bdsb 14456

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-sn 3598  df-bdc 14475

This theorem is referenced by:  bdcpr  14505  bdctp  14506  bdvsn  14508  bdcsuc  14514