Theorem bdcsn 13905

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 13855	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 13884	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3589	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 13879	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2156  {csn 3583  BOUNDED wbdc 13875

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1440  ax-gen 1442  ax-ie1 1486  ax-ie2 1487  ax-4 1503  ax-17 1519  ax-ial 1527  ax-ext 2152  ax-bd0 13848  ax-bdeq 13855  ax-bdsb 13857

This theorem depends on definitions:  df-bi 116  df-clab 2157  df-cleq 2163  df-clel 2166  df-sn 3589  df-bdc 13876

This theorem is referenced by:  bdcpr  13906  bdctp  13907  bdvsn  13909  bdcsuc  13915