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Theorem tpeq3d 3897
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 3894 . 2  |-  ( A  =  B  ->  { C ,  D ,  A }  =  { C ,  D ,  B } )
31, 2syl 16 1  |-  ( ph  ->  { C ,  D ,  A }  =  { C ,  D ,  B } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   {ctp 3816
This theorem is referenced by:  tpeq123d  3898  erngset  31597  erngset-rN  31605
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-7 1749  ax-11 1761  ax-12 1950  ax-ext 2417
This theorem depends on definitions:  df-bi 178  df-or 360  df-an 361  df-tru 1328  df-ex 1551  df-nf 1554  df-sb 1659  df-clab 2423  df-cleq 2429  df-clel 2432  df-nfc 2561  df-v 2958  df-un 3325  df-sn 3820  df-tp 3822
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