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Theorem nabbi 2790
Description: Not equivalent wff's correspond to not equal class abstractions. (Contributed by AV, 7-Apr-2019.) (Proof shortened by Wolf Lammen, 25-Nov-2019.)
Assertion
Ref Expression
nabbi

Proof of Theorem nabbi
StepHypRef Expression
1 df-ne 2654 . 2
2 exnal 1648 . . . 4
3 xor3 357 . . . . 5
43exbii 1667 . . . 4
52, 4bitr3i 251 . . 3
6 abbi 2588 . . 3
75, 6xchnxbi 308 . 2
81, 7bitr2i 250 1
Colors of variables: wff setvar class
Syntax hints:  -.wn 3  <->wb 184  A.wal 1393  =wceq 1395  E.wex 1612  {cab 2442  =/=wne 2652
This theorem is referenced by:  suppvalbr  6922
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
This theorem depends on definitions:  df-bi 185  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-ne 2654
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