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Theorem preq1i 3887
Description: Equality inference for unordered pairs. (Contributed by NM, 19-Oct-2012.)
Hypothesis
Ref Expression
preq1i.1  |-  A  =  B
Assertion
Ref Expression
preq1i  |-  { A ,  C }  =  { B ,  C }

Proof of Theorem preq1i
StepHypRef Expression
1 preq1i.1 . 2  |-  A  =  B
2 preq1 3884 . 2  |-  ( A  =  B  ->  { A ,  C }  =  { B ,  C }
)
31, 2ax-mp 8 1  |-  { A ,  C }  =  { B ,  C }
Colors of variables: wff set class
Syntax hints:    = wceq 1653   {cpr 3816
This theorem is referenced by:  funopg  5486  disjdifprg2  24019  frgraunss  28386  n4cyclfrgra  28409
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2418
This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2424  df-cleq 2430  df-clel 2433  df-nfc 2562  df-v 2959  df-un 3326  df-sn 3821  df-pr 3822
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