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Theorem prneli 4614
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
prneli.1 𝐴𝐵
prneli.2 𝐴𝐶
Assertion
Ref Expression
prneli 𝐴 ∉ {𝐵, 𝐶}

Proof of Theorem prneli
StepHypRef Expression
1 prneli.1 . . 3 𝐴𝐵
2 prneli.2 . . 3 𝐴𝐶
31, 2nelpri 4613 . 2 ¬ 𝐴 ∈ {𝐵, 𝐶}
43nelir 3050 1 𝐴 ∉ {𝐵, 𝐶}
Colors of variables: wff setvar class
Syntax hints:  wne 2941  wnel 3047  {cpr 4586
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2707
This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-tru 1544  df-ex 1782  df-sb 2068  df-clab 2714  df-cleq 2728  df-clel 2814  df-ne 2942  df-nel 3048  df-v 3445  df-un 3913  df-sn 4585  df-pr 4587
This theorem is referenced by:  vdegp1ai  28370
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