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Theorem tpeq3d 4078
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 4075 . 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 1455   {ctp 3984
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1680  ax-4 1693  ax-5 1769  ax-6 1816  ax-7 1862  ax-10 1926  ax-11 1931  ax-12 1944  ax-13 2102  ax-ext 2442
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1458  df-ex 1675  df-nf 1679  df-sb 1809  df-clab 2449  df-cleq 2455  df-clel 2458  df-nfc 2592  df-v 3059  df-un 3421  df-sn 3981  df-tp 3985
This theorem is referenced by:  tpeq123d  4079  fntpb  6153  erngset  34413  erngset-rN  34421
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