Theorem dftp2 3642

Description: Alternate definition of unordered triple of classes. Special case of Definition 5.3 of [TakeutiZaring] p. 16. (Contributed by NM, 8-Apr-1994.)

Assertion

Ref	Expression
dftp2	|- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Distinct variable groups:   x, A   x, B   x, C

Proof of Theorem dftp2

Step	Hyp	Ref	Expression
1		vex 2741	. . 3 |- x e. _V
2	1	eltp 3641	. 2 |- ( x e. { A , B , C } <-> ( x = A \/ x = B \/ x = C ) )
3	2	abbi2i 2292	1 |- { A , B , C } = { x | ( x = A \/ x = B \/ x = C ) }

Syntax hints:   \/ w3o 977   = wceq 1353   {cab 2163   {ctp 3595

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-io 709  ax-5 1447  ax-7 1448  ax-gen 1449  ax-ie1 1493  ax-ie2 1494  ax-8 1504  ax-10 1505  ax-11 1506  ax-i12 1507  ax-bndl 1509  ax-4 1510  ax-17 1526  ax-i9 1530  ax-ial 1534  ax-i5r 1535  ax-ext 2159

This theorem depends on definitions:  df-bi 117  df-3or 979  df-tru 1356  df-nf 1461  df-sb 1763  df-clab 2164  df-cleq 2170  df-clel 2173  df-nfc 2308  df-v 2740  df-un 3134  df-sn 3599  df-pr 3600  df-tp 3601

This theorem is referenced by:  tprot  3686  tpid3g  3708