Theorem bdcsn 16233

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 16183	. . 3 |- BOUNDED y = x
2	1	bdcab 16212	. 2 |- BOUNDED { y | y = x }
3		df-sn 3672	. 2 |- { x } = { y | y = x }
4	2, 3	bdceqir 16207	1 |- BOUNDED { x }

Syntax hints:   {cab 2215   {csn 3666  BOUNDED wbdc 16203

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 1493  ax-gen 1495  ax-ie1 1539  ax-ie2 1540  ax-4 1556  ax-17 1572  ax-ial 1580  ax-ext 2211  ax-bd0 16176  ax-bdeq 16183  ax-bdsb 16185

This theorem depends on definitions:  df-bi 117  df-clab 2216  df-cleq 2222  df-clel 2225  df-sn 3672  df-bdc 16204

This theorem is referenced by:  bdcpr  16234  bdctp  16235  bdvsn  16237  bdcsuc  16243