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Theorem prneli 4576
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 4575 . 2 ¬ 𝐴 ∈ {𝐵, 𝐶}
43nelir 3120 1 𝐴 ∉ {𝐵, 𝐶}
Colors of variables: wff setvar class
Syntax hints:  wne 3013  wnel 3117  {cpr 4550
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 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796
This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-tru 1541  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-ne 3014  df-nel 3118  df-v 3481  df-un 3923  df-sn 4549  df-pr 4551
This theorem is referenced by:  vdegp1ai  27315
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