Theorem bdctp 16898

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 16897	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 16896	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 16888	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3717	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 16870	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

This proof depends on syntax axioms:   ∪ cun 3218  {csn 3709  {cpr 3710  {ctp 3711  BOUNDED wbdc 16866

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1500  ax-gen 1502  ax-ie1 1546  ax-ie2 1547  ax-4 1563  ax-17 1579  ax-ial 1587  ax-ext 2220  ax-bd0 16839  ax-bdor 16842  ax-bdeq 16846  ax-bdsb 16848

This proof depends on definitions:  df-bi 117  df-clab 2225  df-cleq 2231  df-clel 2234  df-un 3224  df-sn 3715  df-pr 3716  df-tp 3717  df-bdc 16867

This theorem is used by: (None)