Theorem bdcsn 16586

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 16536	. . 3 |- BOUNDED y = x
2	1	bdcab 16565	. 2 |- BOUNDED { y | y = x }
3		df-sn 3679	. 2 |- { x } = { y | y = x }
4	2, 3	bdceqir 16560	1 |- BOUNDED { x }

Syntax hints:   {cab 2217   {csn 3673  BOUNDED wbdc 16556

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 1496  ax-gen 1498  ax-ie1 1542  ax-ie2 1543  ax-4 1559  ax-17 1575  ax-ial 1583  ax-ext 2213  ax-bd0 16529  ax-bdeq 16536  ax-bdsb 16538

This theorem depends on definitions:  df-bi 117  df-clab 2218  df-cleq 2224  df-clel 2227  df-sn 3679  df-bdc 16557

This theorem is referenced by:  bdcpr  16587  bdctp  16588  bdvsn  16590  bdcsuc  16596