Theorem bdctp 15369

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 15368	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 15367	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 15359	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3626	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 15341	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Syntax hints:   ∪ cun 3151  {csn 3618  {cpr 3619  {ctp 3620  BOUNDED wbdc 15337

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 1458  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-4 1521  ax-17 1537  ax-ial 1545  ax-ext 2175  ax-bd0 15310  ax-bdor 15313  ax-bdeq 15317  ax-bdsb 15319

This theorem depends on definitions:  df-bi 117  df-clab 2180  df-cleq 2186  df-clel 2189  df-un 3157  df-sn 3624  df-pr 3625  df-tp 3626  df-bdc 15338

This theorem is referenced by: (None)