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Theorem tpeq2d 4114
Description: Equality theorem for unordered triples. (Contributed by NM, 22-Jun-2014.)
Hypothesis
Ref Expression
tpeq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
tpeq2d  |-  ( ph  ->  { C ,  A ,  D }  =  { C ,  B ,  D } )

Proof of Theorem tpeq2d
StepHypRef Expression
1 tpeq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 tpeq2 4111 . 2  |-  ( A  =  B  ->  { C ,  A ,  D }  =  { C ,  B ,  D } )
31, 2syl 16 1  |-  ( ph  ->  { C ,  A ,  D }  =  { C ,  B ,  D } )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    = wceq 1374   {ctp 4026
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1596  ax-4 1607  ax-5 1675  ax-6 1714  ax-7 1734  ax-10 1781  ax-11 1786  ax-12 1798  ax-13 1963  ax-ext 2440
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1377  df-ex 1592  df-nf 1595  df-sb 1707  df-clab 2448  df-cleq 2454  df-clel 2457  df-nfc 2612  df-v 3110  df-un 3476  df-sn 4023  df-pr 4025  df-tp 4027
This theorem is referenced by:  tpeq123d  4116  erngset  35473  erngset-rN  35481
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