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Theorem difsnb 3663
 Description: equals if and only if is not a member of . Generalization of difsn 3657. (Contributed by David Moews, 1-May-2017.)
Assertion
Ref Expression
difsnb

Proof of Theorem difsnb
StepHypRef Expression
1 difsn 3657 . 2
2 neldifsnd 3654 . . . . 5
3 nelne1 2398 . . . . 5
42, 3mpdan 417 . . . 4
54necomd 2394 . . 3
65necon2bi 2363 . 2
71, 6impbii 125 1
 Colors of variables: wff set class Syntax hints:   wn 3   wb 104   wceq 1331   wcel 1480   wne 2308   cdif 3068  csn 3527 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-in1 603  ax-in2 604  ax-io 698  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-10 1483  ax-11 1484  ax-i12 1485  ax-bndl 1486  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132  df-clel 2135  df-nfc 2270  df-ne 2309  df-v 2688  df-dif 3073  df-sn 3533 This theorem is referenced by: (None)
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