Theorem bdcsn 15006

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 14956	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 14985	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3613	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 14980	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2175  {csn 3607  BOUNDED wbdc 14976

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2171  ax-bd0 14949  ax-bdeq 14956  ax-bdsb 14958

This theorem depends on definitions:  df-bi 117  df-clab 2176  df-cleq 2182  df-clel 2185  df-sn 3613  df-bdc 14977

This theorem is referenced by:  bdcpr  15007  bdctp  15008  bdvsn  15010  bdcsuc  15016