Theorem bdctp 11120

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 11119	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 11118	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 11110	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3433	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 11092	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Syntax hints:   ∪ cun 2984  {csn 3425  {cpr 3426  {ctp 3427  BOUNDED wbdc 11088

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1379  ax-gen 1381  ax-ie1 1425  ax-ie2 1426  ax-4 1443  ax-17 1462  ax-ial 1470  ax-ext 2067  ax-bd0 11061  ax-bdor 11064  ax-bdeq 11068  ax-bdsb 11070

This theorem depends on definitions:  df-bi 115  df-clab 2072  df-cleq 2078  df-clel 2081  df-un 2990  df-sn 3431  df-pr 3432  df-tp 3433  df-bdc 11089

This theorem is referenced by: (None)