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Theorem difin2 3430
 Description: Represent a set difference as an intersection with a larger difference. (Contributed by Jeff Madsen, 2-Sep-2009.)
Assertion
Ref Expression
difin2

Proof of Theorem difin2
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 ssel 3174 . . . . 5
21pm4.71d 615 . . . 4
32anbi1d 685 . . 3
4 eldif 3162 . . 3
5 elin 3358 . . . 4
6 eldif 3162 . . . . 5
76anbi1i 676 . . . 4
8 ancom 437 . . . . 5
9 anass 630 . . . . 5
108, 9bitr4i 243 . . . 4
115, 7, 103bitri 262 . . 3
123, 4, 113bitr4g 279 . 2
1312eqrdv 2281 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 358   wceq 1623   wcel 1684   cdif 3149   cin 3151   wss 3152 This theorem is referenced by:  issubdrg  15570  restcld  16903  limcnlp  19228  ballotlemfp1  23050  difelsiga  23494  difin2OLD  26361 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603  ax-9 1635  ax-8 1643  ax-6 1703  ax-7 1708  ax-11 1715  ax-12 1866  ax-ext 2264 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-tru 1310  df-ex 1529  df-nf 1532  df-sb 1630  df-clab 2270  df-cleq 2276  df-clel 2279  df-nfc 2408  df-v 2790  df-dif 3155  df-in 3159  df-ss 3166
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