Theorem bdcsn 14810

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 14760	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 14789	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3600	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 14784	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2163  {csn 3594  BOUNDED wbdc 14780

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 1447  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-4 1510  ax-17 1526  ax-ial 1534  ax-ext 2159  ax-bd0 14753  ax-bdeq 14760  ax-bdsb 14762

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-sn 3600  df-bdc 14781

This theorem is referenced by:  bdcpr  14811  bdctp  14812  bdvsn  14814  bdcsuc  14820