Theorem bdcsn 15670

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 15620	. . 3 ⊢ BOUNDED 𝑦 = 𝑥
2	1	bdcab 15649	. 2 ⊢ BOUNDED {𝑦 ∣ 𝑦 = 𝑥}
3		df-sn 3638	. 2 ⊢ {𝑥} = {𝑦 ∣ 𝑦 = 𝑥}
4	2, 3	bdceqir 15644	1 ⊢ BOUNDED {𝑥}

Syntax hints:  {cab 2190  {csn 3632  BOUNDED wbdc 15640

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 1469  ax-gen 1471  ax-ie1 1515  ax-ie2 1516  ax-4 1532  ax-17 1548  ax-ial 1556  ax-ext 2186  ax-bd0 15613  ax-bdeq 15620  ax-bdsb 15622

This theorem depends on definitions:  df-bi 117  df-clab 2191  df-cleq 2197  df-clel 2200  df-sn 3638  df-bdc 15641

This theorem is referenced by:  bdcpr  15671  bdctp  15672  bdvsn  15674  bdcsuc  15680