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Theorem tpeq1d 4075
Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)
Hypothesis
Ref Expression
tpeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
tpeq1d  |-  ( ph  ->  { A ,  C ,  D }  =  { B ,  C ,  D } )

Proof of Theorem tpeq1d
StepHypRef Expression
1 tpeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 tpeq1 4072 . 2  |-  ( A  =  B  ->  { A ,  C ,  D }  =  { B ,  C ,  D } )
31, 2syl 17 1  |-  ( ph  ->  { A ,  C ,  D }  =  { B ,  C ,  D } )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1454   {ctp 3983
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768  ax-6 1815  ax-7 1861  ax-10 1925  ax-11 1930  ax-12 1943  ax-13 2101  ax-ext 2441
This theorem depends on definitions:  df-bi 190  df-or 376  df-an 377  df-tru 1457  df-ex 1674  df-nf 1678  df-sb 1808  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2591  df-v 3058  df-un 3420  df-sn 3980  df-pr 3982  df-tp 3984
This theorem is referenced by:  tpeq123d  4078
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