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Theorem preq1d 3881
Description: Equality deduction for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypothesis
Ref Expression
preq1d.1  |-  ( ph  ->  A  =  B )
Assertion
Ref Expression
preq1d  |-  ( ph  ->  { A ,  C }  =  { B ,  C } )

Proof of Theorem preq1d
StepHypRef Expression
1 preq1d.1 . 2  |-  ( ph  ->  A  =  B )
2 preq1 3875 . 2  |-  ( A  =  B  ->  { A ,  C }  =  { B ,  C }
)
31, 2syl 16 1  |-  ( ph  ->  { A ,  C }  =  { B ,  C } )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1652   {cpr 3807
This theorem is referenced by:  opthwiener  4450  fprg  5907  dfac2  8003  2pthoncl  21595  eupath2lem3  21693  fprb  25389  wopprc  27092  frgraunss  28322  frgra1v  28325  frgra2v  28326  frgra3v  28329  n4cyclfrgra  28345
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 2416
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 2422  df-cleq 2428  df-clel 2431  df-nfc 2560  df-v 2950  df-un 3317  df-sn 3812  df-pr 3813
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