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Theorem prneli 3499
Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair, using 
e/. (Contributed by David A. Wheeler, 10-May-2015.)
Hypotheses
Ref Expression
prneli.1  |-  A  =/= 
B
prneli.2  |-  A  =/= 
C
Assertion
Ref Expression
prneli  |-  A  e/  { B ,  C }

Proof of Theorem prneli
StepHypRef Expression
1 prneli.1 . . 3  |-  A  =/= 
B
2 prneli.2 . . 3  |-  A  =/= 
C
31, 2nelpri 3498 . 2  |-  -.  A  e.  { B ,  C }
43nelir 2365 1  |-  A  e/  { B ,  C }
Colors of variables: wff set class
Syntax hints:    =/= wne 2267    e/ wnel 2362   {cpr 3475
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 584  ax-in2 585  ax-io 671  ax-5 1391  ax-7 1392  ax-gen 1393  ax-ie1 1437  ax-ie2 1438  ax-8 1450  ax-10 1451  ax-11 1452  ax-i12 1453  ax-bndl 1454  ax-4 1455  ax-17 1474  ax-i9 1478  ax-ial 1482  ax-i5r 1483  ax-ext 2082
This theorem depends on definitions:  df-bi 116  df-tru 1302  df-nf 1405  df-sb 1704  df-clab 2087  df-cleq 2093  df-clel 2096  df-nfc 2229  df-ne 2268  df-nel 2363  df-v 2643  df-un 3025  df-sn 3480  df-pr 3481
This theorem is referenced by: (None)
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