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Theorem preq1i 3722
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 3719 . 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 1632   {cpr 3654
This theorem is referenced by:  funopg  5302  disjdifprg2  23368  n4cyclfrgra  28440
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277
This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535  df-sb 1639  df-clab 2283  df-cleq 2289  df-clel 2292  df-nfc 2421  df-v 2803  df-un 3170  df-sn 3659  df-pr 3660
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