Theorem bdcsn 16005

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 15955	. . 3 |- BOUNDED y = x
2	1	bdcab 15984	. 2 |- BOUNDED { y | y = x }
3		df-sn 3649	. 2 |- { x } = { y | y = x }
4	2, 3	bdceqir 15979	1 |- BOUNDED { x }

Syntax hints:   {cab 2193   {csn 3643  BOUNDED wbdc 15975

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558  ax-ext 2189  ax-bd0 15948  ax-bdeq 15955  ax-bdsb 15957

This theorem depends on definitions:  df-bi 117  df-clab 2194  df-cleq 2200  df-clel 2203  df-sn 3649  df-bdc 15976

This theorem is referenced by:  bdcpr  16006  bdctp  16007  bdvsn  16009  bdcsuc  16015