Theorem bdctp 14395

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 14394	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 14393	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 14385	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3600	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 14367	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Syntax hints:   ∪ cun 3127  {csn 3592  {cpr 3593  {ctp 3594  BOUNDED wbdc 14363

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 14336  ax-bdor 14339  ax-bdeq 14343  ax-bdsb 14345

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3133  df-sn 3598  df-pr 3599  df-tp 3600  df-bdc 14364

This theorem is referenced by: (None)