Theorem bdcsn 13239

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 13189	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 13218	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3538	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 13213	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2126  {csn 3532  BOUNDED wbdc 13209

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 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-4 1488  ax-17 1507  ax-ial 1515  ax-ext 2122  ax-bd0 13182  ax-bdeq 13189  ax-bdsb 13191

This theorem depends on definitions:  df-bi 116  df-clab 2127  df-cleq 2133  df-clel 2136  df-sn 3538  df-bdc 13210

This theorem is referenced by:  bdcpr  13240  bdctp  13241  bdvsn  13243  bdcsuc  13249