Theorem bdcsn 16810

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 16760	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 16789	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3711	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 16784	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2224  {csn 3705  BOUNDED wbdc 16780

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 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-bd0 16753  ax-bdeq 16760  ax-bdsb 16762

This theorem depends on definitions:  df-bi 117  df-clab 2225  df-cleq 2231  df-clel 2234  df-sn 3711  df-bdc 16781

This theorem is referenced by:  bdcpr  16811  bdctp  16812  bdvsn  16814  bdcsuc  16820