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Theorem tpeq2d 3719
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 3716 . 2  |-  ( A  =  B  ->  { C ,  A ,  D }  =  { C ,  B ,  D } )
31, 2syl 15 1  |-  ( ph  ->  { C ,  A ,  D }  =  { C ,  B ,  D } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1623   {ctp 3642
This theorem is referenced by:  tpeq123d  3721  erngset  30989  erngset-rN  30997
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-un 3157  df-sn 3646  df-pr 3647  df-tp 3648
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