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Theorem difundi 3217
 Description: Distributive law for class difference. Theorem 39 of [Suppes] p. 29. (Contributed by NM, 17-Aug-2004.)
Assertion
Ref Expression
difundi

Proof of Theorem difundi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 eldif 2955 . . . 4
2 eldif 2955 . . . 4
31, 2anbi12i 441 . . 3
4 elin 3154 . . 3
5 eldif 2955 . . . . . 6
6 elun 3112 . . . . . . . 8
76notbii 604 . . . . . . 7
87anbi2i 438 . . . . . 6
95, 8bitri 177 . . . . 5
10 ioran 679 . . . . . 6
1110anbi2i 438 . . . . 5
129, 11bitri 177 . . . 4
13 anandi 532 . . . 4
1412, 13bitri 177 . . 3
153, 4, 143bitr4ri 206 . 2
1615eqriv 2053 1
 Colors of variables: wff set class Syntax hints:   wn 3   wa 101   wo 639   wceq 1259   wcel 1409   cdif 2942   cun 2943   cin 2944 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-in1 554  ax-in2 555  ax-io 640  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-10 1412  ax-11 1413  ax-i12 1414  ax-bndl 1415  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443  ax-i5r 1444  ax-ext 2038 This theorem depends on definitions:  df-bi 114  df-tru 1262  df-nf 1366  df-sb 1662  df-clab 2043  df-cleq 2049  df-clel 2052  df-nfc 2183  df-v 2576  df-dif 2948  df-un 2950  df-in 2952 This theorem is referenced by:  undm  3223
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