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Theorem difin2 3516
 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 3267 . . . . 5
21pm4.71d 615 . . . 4
32anbi1d 685 . . 3
4 eldif 3221 . . 3
5 elin 3219 . . . 4
6 eldif 3221 . . . . 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 2351 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wa 358   wceq 1642   wcel 1710   cdif 3206   cin 3208   wss 3257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334 This theorem depends on definitions:  df-bi 177  df-or 359  df-an 360  df-nan 1288  df-tru 1319  df-ex 1542  df-nf 1545  df-sb 1649  df-clab 2340  df-cleq 2346  df-clel 2349  df-nfc 2478  df-v 2861  df-nin 3211  df-compl 3212  df-in 3213  df-dif 3215  df-ss 3259 This theorem is referenced by: (None)
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