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Theorem raldifb 3643
 Description: Restricted universal quantification on a class difference in terms of an implication. (Contributed by Alexander van der Vekens, 3-Jan-2018.)
Assertion
Ref Expression
raldifb

Proof of Theorem raldifb
StepHypRef Expression
1 impexp 446 . . . 4
21bicomi 202 . . 3
3 df-nel 2655 . . . . . 6
43anbi2i 694 . . . . 5
5 eldif 3485 . . . . . 6
65bicomi 202 . . . . 5
74, 6bitri 249 . . . 4
87imbi1i 325 . . 3
92, 8bitri 249 . 2
109ralbii2 2886 1
 Colors of variables: wff setvar class Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  e.wcel 1818  e/wnel 2653  A.wral 2807  \cdif 3472 This theorem is referenced by:  raldifsnb  4161  cusgrares  24472  2spotdisj  25061  aacllem  33216 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-nel 2655  df-ral 2812  df-v 3111  df-dif 3478
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