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Theorem raldifb 3585
 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 204 . . 3
3 df-nel 2603 . . . . . 6
43anbi2i 694 . . . . 5
5 eldif 3426 . . . . . 6
65bicomi 204 . . . . 5
74, 6bitri 251 . . . 4
87imbi1i 325 . . 3
92, 8bitri 251 . 2
109ralbii2 2835 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 186   wa 369   wcel 1844   wnel 2601  wral 2756   cdif 3413 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1641  ax-4 1654  ax-5 1727  ax-6 1773  ax-7 1816  ax-10 1863  ax-11 1868  ax-12 1880  ax-13 2028  ax-ext 2382 This theorem depends on definitions:  df-bi 187  df-an 371  df-tru 1410  df-ex 1636  df-nf 1640  df-sb 1766  df-clab 2390  df-cleq 2396  df-clel 2399  df-nfc 2554  df-nel 2603  df-ral 2761  df-v 3063  df-dif 3419 This theorem is referenced by:  raldifsnb  4105  cusgrares  24901  2spotdisj  25490  aacllem  38873
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