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Theorem tpeq3d 4064
Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)
Hypothesis
Ref Expression
tpeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
tpeq3d  |-  ( ph  ->  { C ,  D ,  A }  =  { C ,  D ,  B } )

Proof of Theorem tpeq3d
StepHypRef Expression
1 tpeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 tpeq3 4061 . 2  |-  ( A  =  B  ->  { C ,  D ,  A }  =  { C ,  D ,  B } )
31, 2syl 17 1  |-  ( ph  ->  { C ,  D ,  A }  =  { C ,  D ,  B } )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1405   {ctp 3975
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1639  ax-4 1652  ax-5 1725  ax-6 1771  ax-7 1814  ax-10 1861  ax-11 1866  ax-12 1878  ax-13 2026  ax-ext 2380
This theorem depends on definitions:  df-bi 185  df-or 368  df-an 369  df-tru 1408  df-ex 1634  df-nf 1638  df-sb 1764  df-clab 2388  df-cleq 2394  df-clel 2397  df-nfc 2552  df-v 3060  df-un 3418  df-sn 3972  df-tp 3976
This theorem is referenced by:  tpeq123d  4065  erngset  33799  erngset-rN  33807
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