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Theorem indifdir 3511
 Description: Distribute intersection over difference. (Contributed by Scott Fenton, 14-Apr-2011.)
Assertion
Ref Expression
indifdir

Proof of Theorem indifdir
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 pm3.24 852 . . . . . . . 8
21intnan 880 . . . . . . 7
3 anass 630 . . . . . . 7
42, 3mtbir 290 . . . . . 6
54biorfi 396 . . . . 5
6 an32 773 . . . . 5
7 andi 837 . . . . 5
85, 6, 73bitr4i 268 . . . 4
9 ianor 474 . . . . 5
109anbi2i 675 . . . 4
118, 10bitr4i 243 . . 3
12 elin 3219 . . . 4
13 eldif 3221 . . . . 5
1413anbi1i 676 . . . 4
1512, 14bitri 240 . . 3
16 eldif 3221 . . . 4
17 elin 3219 . . . . 5
18 elin 3219 . . . . . 6
1918notbii 287 . . . . 5
2017, 19anbi12i 678 . . . 4
2116, 20bitri 240 . . 3
2211, 15, 213bitr4i 268 . 2
2322eqriv 2350 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wo 357   wa 358   wceq 1642   wcel 1710   cdif 3206   cin 3208 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 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 This theorem is referenced by: (None)
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