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Theorem AnelBC 26923
 Description: If an element doesn't match the items in an unordered pair, it is not in the unordered pair, using . (Contributed by David A. Wheeler, 10-May-2015.)
Hypotheses
Ref Expression
AnelBC.1
AnelBC.2
Assertion
Ref Expression
AnelBC

Proof of Theorem AnelBC
StepHypRef Expression
1 AnelBC.1 . . 3
2 AnelBC.2 . . 3
31, 2nelpri 3565 . 2
4 df-nel 2415 . 2
53, 4mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wn 5   wcel 1621   wne 2412   wnel 2413  cpr 3545 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-7 1535  ax-gen 1536  ax-8 1623  ax-11 1624  ax-17 1628  ax-12o 1664  ax-10 1678  ax-9 1684  ax-4 1692  ax-16 1926  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1315  df-ex 1538  df-nf 1540  df-sb 1883  df-clab 2240  df-cleq 2246  df-clel 2249  df-nfc 2374  df-ne 2414  df-nel 2415  df-v 2729  df-un 3083  df-sn 3550  df-pr 3551
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