Theorem bdcsn 9305

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 9255	. . 3 ⊢ BOUNDED y = x
2	1	bdcab 9284	. 2 ⊢ BOUNDED {y ∣ y = x}
3		df-sn 3373	. 2 ⊢ {x} = {y ∣ y = x}
4	2, 3	bdceqir 9279	1 ⊢ BOUNDED {x}

Syntax hints:  {cab 2023  {csn 3367  BOUNDED wbdc 9275

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-4 1397  ax-17 1416  ax-ial 1424  ax-ext 2019  ax-bd0 9248  ax-bdeq 9255  ax-bdsb 9257

This theorem depends on definitions:  df-bi 110  df-clab 2024  df-cleq 2030  df-clel 2033  df-sn 3373  df-bdc 9276

This theorem is referenced by:  bdcpr  9306  bdctp  9307  bdvsn  9309  bdcsuc  9315