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Theorem difin2 3605
 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 3344 . . . . 5
21pm4.71d 617 . . . 4
32anbi1d 687 . . 3
4 eldif 3332 . . 3
5 elin 3532 . . . 4
6 eldif 3332 . . . . 5
76anbi1i 678 . . . 4
8 ancom 439 . . . . 5
9 anass 632 . . . . 5
108, 9bitr4i 245 . . . 4
115, 7, 103bitri 264 . . 3
123, 4, 113bitr4g 281 . 2
1312eqrdv 2436 1
 Colors of variables: wff set class Syntax hints:   wn 3   wi 4   wa 360   wceq 1653   wcel 1726   cdif 3319   cin 3321   wss 3322 This theorem is referenced by:  issubdrg  15895  restcld  17238  limcnlp  19767  difelsiga  24518  ballotlemfp1  24751 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1556  ax-5 1567  ax-17 1627  ax-9 1667  ax-8 1688  ax-6 1745  ax-7 1750  ax-11 1762  ax-12 1951  ax-ext 2419 This theorem depends on definitions:  df-bi 179  df-or 361  df-an 362  df-tru 1329  df-ex 1552  df-nf 1555  df-sb 1660  df-clab 2425  df-cleq 2431  df-clel 2434  df-nfc 2563  df-v 2960  df-dif 3325  df-in 3329  df-ss 3336
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