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Theorem notzfaus 4577
 Description: In the Separation Scheme zfauscl 4526, we require that not occur in (which can be generalized to "not be free in"). Here we show special cases of and that result in a contradiction by violating this requirement. (Contributed by NM, 8-Feb-2006.)
Hypotheses
Ref Expression
notzfaus.1
notzfaus.2
Assertion
Ref Expression
notzfaus
Distinct variable group:   ,
Allowed substitution hints:   (,)   ()

Proof of Theorem notzfaus
StepHypRef Expression
1 notzfaus.1 . . . . . 6
2 0ex 4534 . . . . . . 7
32snnz 4089 . . . . . 6
41, 3eqnetri 2693 . . . . 5
5 n0 3740 . . . . 5
64, 5mpbi 212 . . . 4
7 biimt 337 . . . . . 6
8 iman 426 . . . . . . 7
9 notzfaus.2 . . . . . . . 8
109anbi2i 699 . . . . . . 7
118, 10xchbinxr 313 . . . . . 6
127, 11syl6bb 265 . . . . 5
13 xor3 359 . . . . 5
1412, 13sylibr 216 . . . 4
156, 14eximii 1708 . . 3
16 exnal 1698 . . 3
1715, 16mpbi 212 . 2
1817nex 1677 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wi 4   wb 188   wa 371  wal 1441   wceq 1443  wex 1662   wcel 1886   wne 2621  c0 3730  csn 3967 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1668  ax-4 1681  ax-5 1757  ax-6 1804  ax-7 1850  ax-10 1914  ax-11 1919  ax-12 1932  ax-13 2090  ax-ext 2430  ax-nul 4533 This theorem depends on definitions:  df-bi 189  df-or 372  df-an 373  df-tru 1446  df-ex 1663  df-nf 1667  df-sb 1797  df-clab 2437  df-cleq 2443  df-clel 2446  df-nfc 2580  df-ne 2623  df-v 3046  df-dif 3406  df-nul 3731  df-sn 3968 This theorem is referenced by: (None)
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