Theorem bdcsn 15624

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 15574	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 15603	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3629	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 15598	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2182  {csn 3623  BOUNDED wbdc 15594

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 1461  ax-gen 1463  ax-ie1 1507  ax-ie2 1508  ax-4 1524  ax-17 1540  ax-ial 1548  ax-ext 2178  ax-bd0 15567  ax-bdeq 15574  ax-bdsb 15576

This theorem depends on definitions:  df-bi 117  df-clab 2183  df-cleq 2189  df-clel 2192  df-sn 3629  df-bdc 15595

This theorem is referenced by:  bdcpr  15625  bdctp  15626  bdvsn  15628  bdcsuc  15634