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Theorem raldifsni 4160
Description: Rearrangement of a property of a singleton difference. (Contributed by Stefan O'Rear, 27-Feb-2015.)
Assertion
Ref Expression
raldifsni

Proof of Theorem raldifsni
StepHypRef Expression
1 eldifsn 4155 . . . 4
21imbi1i 325 . . 3
3 impexp 446 . . 3
4 df-ne 2654 . . . . . 6
54imbi1i 325 . . . . 5
6 con34b 292 . . . . 5
75, 6bitr4i 252 . . . 4
87imbi2i 312 . . 3
92, 3, 83bitri 271 . 2
109ralbii2 2886 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  =wceq 1395  e.wcel 1818  =/=wne 2652  A.wral 2807  \cdif 3472  {csn 4029
This theorem is referenced by:  islindf4  18873  snlindsntor  33072
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-ral 2812  df-v 3111  df-dif 3478  df-sn 4030
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