Theorem bdcsn 14975

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 14925	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 14954	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3610	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 14949	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2173  {csn 3604  BOUNDED wbdc 14945

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-17 1536  ax-ial 1544  ax-ext 2169  ax-bd0 14918  ax-bdeq 14925  ax-bdsb 14927

This theorem depends on definitions:  df-bi 117  df-clab 2174  df-cleq 2180  df-clel 2183  df-sn 3610  df-bdc 14946

This theorem is referenced by:  bdcpr  14976  bdctp  14977  bdvsn  14979  bdcsuc  14985