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Theorem prneli 3632
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 3631 . 2  |-  -.  A  e.  { B ,  C }
43nelir 2458 1  |-  A  e/  { B ,  C }
Colors of variables: wff set class
Syntax hints:    =/= wne 2360    e/ wnel 2455   {cpr 3608
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-in1 615  ax-in2 616  ax-io 710  ax-5 1458  ax-7 1459  ax-gen 1460  ax-ie1 1504  ax-ie2 1505  ax-8 1515  ax-10 1516  ax-11 1517  ax-i12 1518  ax-bndl 1520  ax-4 1521  ax-17 1537  ax-i9 1541  ax-ial 1545  ax-i5r 1546  ax-ext 2171
This theorem depends on definitions:  df-bi 117  df-tru 1367  df-nf 1472  df-sb 1774  df-clab 2176  df-cleq 2182  df-clel 2185  df-nfc 2321  df-ne 2361  df-nel 2456  df-v 2754  df-un 3148  df-sn 3613  df-pr 3614
This theorem is referenced by: (None)
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