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Theorem notzfaus 4627
Description: In the Separation Scheme zfauscl 4575, 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:   ,

Proof of Theorem notzfaus
StepHypRef Expression
1 notzfaus.1 . . . . . 6
2 0ex 4582 . . . . . . 7
32snnz 4148 . . . . . 6
41, 3eqnetri 2753 . . . . 5
5 n0 3794 . . . . 5
64, 5mpbi 208 . . . 4
7 biimt 335 . . . . . 6
8 iman 424 . . . . . . 7
9 notzfaus.2 . . . . . . . 8
109anbi2i 694 . . . . . . 7
118, 10xchbinxr 311 . . . . . 6
127, 11syl6bb 261 . . . . 5
13 xor3 357 . . . . 5
1412, 13sylibr 212 . . . 4
156, 14eximii 1658 . . 3
16 exnal 1648 . . 3
1715, 16mpbi 208 . 2
1817nex 1627 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  ->wi 4  <->wb 184  /\wa 369  A.wal 1393  =wceq 1395  E.wex 1612  e.wcel 1818  =/=wne 2652   c0 3784  {csn 4029
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1618  ax-4 1631  ax-5 1704  ax-6 1747  ax-7 1790  ax-10 1837  ax-11 1842  ax-12 1854  ax-13 1999  ax-ext 2435  ax-nul 4581
This theorem depends on definitions:  df-bi 185  df-or 370  df-an 371  df-tru 1398  df-ex 1613  df-nf 1617  df-sb 1740  df-clab 2443  df-cleq 2449  df-clel 2452  df-nfc 2607  df-ne 2654  df-v 3111  df-dif 3478  df-nul 3785  df-sn 4030
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