Theorem bdctp 14627

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 14626	. . 3 ⊢ BOUNDED {𝑥, 𝑦}
2		bdcsn 14625	. . 3 ⊢ BOUNDED {𝑧}
3	1, 2	bdcun 14617	. 2 ⊢ BOUNDED ({𝑥, 𝑦} ∪ {𝑧})
4		df-tp 3601	. 2 ⊢ {𝑥, 𝑦, 𝑧} = ({𝑥, 𝑦} ∪ {𝑧})
5	3, 4	bdceqir 14599	1 ⊢ BOUNDED {𝑥, 𝑦, 𝑧}

Syntax hints:   ∪ cun 3128  {csn 3593  {cpr 3594  {ctp 3595  BOUNDED wbdc 14595

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 14568  ax-bdor 14571  ax-bdeq 14575  ax-bdsb 14577

This theorem depends on definitions:  df-bi 117  df-clab 2164  df-cleq 2170  df-clel 2173  df-un 3134  df-sn 3599  df-pr 3600  df-tp 3601  df-bdc 14596

This theorem is referenced by: (None)