Theorem bdcsn 13068

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 13018	. . 3 |- BOUNDED y = x
2	1	bdcab 13047	. 2 |- BOUNDED { y | y = x }
3		df-sn 3533	. 2 |- { x } = { y | y = x }
4	2, 3	bdceqir 13042	1 |- BOUNDED { x }

Syntax hints:   {cab 2125   {csn 3527  BOUNDED wbdc 13038

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-bd0 13011  ax-bdeq 13018  ax-bdsb 13020

This theorem depends on definitions:  df-bi 116  df-clab 2126  df-cleq 2132  df-clel 2135  df-sn 3533  df-bdc 13039

This theorem is referenced by:  bdcpr  13069  bdctp  13070  bdvsn  13072  bdcsuc  13078