Theorem bdcsuc 13078

Description: The successor of a setvar is a bounded class. (Contributed by BJ, 16-Oct-2019.)

Assertion

Ref	Expression
bdcsuc	⊢ BOUNDED suc 𝑥

Proof of Theorem bdcsuc

Step	Hyp	Ref	Expression
1		bdcv 13046	. . 3 ⊢ BOUNDED 𝑥
2		bdcsn 13068	. . 3 ⊢ BOUNDED {𝑥}
3	1, 2	bdcun 13060	. 2 ⊢ BOUNDED (𝑥 ∪ {𝑥})
4		df-suc 4293	. 2 ⊢ suc 𝑥 = (𝑥 ∪ {𝑥})
5	3, 4	bdceqir 13042	1 ⊢ BOUNDED suc 𝑥

Syntax hints:   ∪ cun 3069  {csn 3527  suc csuc 4287  BOUNDED wbdc 13038

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 1423  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-4 1487  ax-17 1506  ax-ial 1514  ax-ext 2121  ax-bd0 13011  ax-bdor 13014  ax-bdeq 13018  ax-bdel 13019  ax-bdsb 13020

This theorem depends on definitions:  df-bi 116  df-clab 2126  df-cleq 2132  df-clel 2135  df-un 3075  df-sn 3533  df-suc 4293  df-bdc 13039

This theorem is referenced by:  bdeqsuc  13079