Theorem bdcsuc 14928

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 14896	. . 3 ⊢ BOUNDED 𝑥
2		bdcsn 14918	. . 3 ⊢ BOUNDED {𝑥}
3	1, 2	bdcun 14910	. 2 ⊢ BOUNDED (𝑥 ∪ {𝑥})
4		df-suc 4383	. 2 ⊢ suc 𝑥 = (𝑥 ∪ {𝑥})
5	3, 4	bdceqir 14892	1 ⊢ BOUNDED suc 𝑥

Syntax hints:   ∪ cun 3139  {csn 3604  suc csuc 4377  BOUNDED wbdc 14888

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 1457  ax-gen 1459  ax-ie1 1503  ax-ie2 1504  ax-4 1520  ax-17 1536  ax-ial 1544  ax-ext 2169  ax-bd0 14861  ax-bdor 14864  ax-bdeq 14868  ax-bdel 14869  ax-bdsb 14870

This theorem depends on definitions:  df-bi 117  df-clab 2174  df-cleq 2180  df-clel 2183  df-un 3145  df-sn 3610  df-suc 4383  df-bdc 14889

This theorem is referenced by:  bdeqsuc  14929