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Theorem tpeq3 3730
 Description: Equality theorem for unordered triples. (Contributed by NM, 13-Sep-2011.)
Assertion
Ref Expression
tpeq3

Proof of Theorem tpeq3
StepHypRef Expression
1 sneq 3664 . . 3
21uneq2d 3342 . 2
3 df-tp 3661 . 2
4 df-tp 3661 . 2
52, 3, 43eqtr4g 2353 1
 Colors of variables: wff set class Syntax hints:   wi 4   wceq 1632   cun 3163  csn 3653  cpr 3654  ctp 3655 This theorem is referenced by:  tpeq3d  3733  fztpval  10861  tpssg  25035  isibg2aa  26215  isibg2aalem2  26217  tppreq3  28181  hashtpg  28217  dvh4dimN  32259 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-tp 3661
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