Theorem bdctp 16467

Description: The unordered triple of three setvars is bounded. (Contributed by BJ, 16-Oct-2019.)

Assertion

Ref	Expression
bdctp	⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Proof of Theorem bdctp

Step	Hyp	Ref	Expression
1		bdcpr 16466	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 16465	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 16457	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3677	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 16439	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Syntax hints:   ∪ cun 3198  {csn 3669  {cpr 3670  {ctp 3671  BOUNDED wbdc 16435

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 1495  ax-gen 1497  ax-ie1 1541  ax-ie2 1542  ax-4 1558  ax-17 1574  ax-ial 1582  ax-ext 2213  ax-bd0 16408  ax-bdor 16411  ax-bdeq 16415  ax-bdsb 16417

This theorem depends on definitions:  df-bi 117  df-clab 2218  df-cleq 2224  df-clel 2227  df-un 3204  df-sn 3675  df-pr 3676  df-tp 3677  df-bdc 16436

This theorem is referenced by: (None)