Theorem bdcsn 15806

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 15756	. . 3 |- BOUNDED y = x
2	1	bdcab 15785	. 2 |- BOUNDED { y | y = x }
3		df-sn 3639	. 2 |- { x } = { y | y = x }
4	2, 3	bdceqir 15780	1 |- BOUNDED { x }

Syntax hints:   {cab 2191   {csn 3633  BOUNDED wbdc 15776

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 1470  ax-gen 1472  ax-ie1 1516  ax-ie2 1517  ax-4 1533  ax-17 1549  ax-ial 1557  ax-ext 2187  ax-bd0 15749  ax-bdeq 15756  ax-bdsb 15758

This theorem depends on definitions:  df-bi 117  df-clab 2192  df-cleq 2198  df-clel 2201  df-sn 3639  df-bdc 15777

This theorem is referenced by:  bdcpr  15807  bdctp  15808  bdvsn  15810  bdcsuc  15816