Theorem bdcsuc 14717

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 14685	. . 3 ⊢ BOUNDED 𝑥
2		bdcsn 14707	. . 3 ⊢ BOUNDED {𝑥}
3	1, 2	bdcun 14699	. 2 ⊢ BOUNDED (𝑥 ∪ {𝑥})
4		df-suc 4373	. 2 ⊢ suc 𝑥 = (𝑥 ∪ {𝑥})
5	3, 4	bdceqir 14681	1 ⊢ BOUNDED suc 𝑥

Syntax hints:   ∪ cun 3129  {csn 3594  suc csuc 4367  BOUNDED wbdc 14677

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 14650  ax-bdor 14653  ax-bdeq 14657  ax-bdel 14658  ax-bdsb 14659

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3135  df-sn 3600  df-suc 4373  df-bdc 14678

This theorem is referenced by:  bdeqsuc  14718