Theorem bdctp 15946

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 15945	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 15944	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 15936	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3646	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 15918	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Syntax hints:   ∪ cun 3168  {csn 3638  {cpr 3639  {ctp 3640  BOUNDED wbdc 15914

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 1471  ax-gen 1473  ax-ie1 1517  ax-ie2 1518  ax-4 1534  ax-17 1550  ax-ial 1558  ax-ext 2188  ax-bd0 15887  ax-bdor 15890  ax-bdeq 15894  ax-bdsb 15896

This theorem depends on definitions:  df-bi 117  df-clab 2193  df-cleq 2199  df-clel 2202  df-un 3174  df-sn 3644  df-pr 3645  df-tp 3646  df-bdc 15915

This theorem is referenced by: (None)