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Theorem tpeq1d 4034
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 4031 . 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 1437   {ctp 3945
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1663  ax-4 1676  ax-5 1752  ax-6 1798  ax-7 1843  ax-10 1891  ax-11 1896  ax-12 1909  ax-13 2063  ax-ext 2408
This theorem depends on definitions:  df-bi 188  df-or 371  df-an 372  df-tru 1440  df-ex 1658  df-nf 1662  df-sb 1791  df-clab 2415  df-cleq 2421  df-clel 2424  df-nfc 2558  df-v 3024  df-un 3384  df-sn 3942  df-pr 3944  df-tp 3946
This theorem is referenced by:  tpeq123d  4037
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