Metamath Proof Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  MPE Home  >  Th. List  >  nabbi Structured version   Unicode version

Theorem nabbi 2758
 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 2620 . 2
2 exnal 1695 . . . 4
3 xor3 358 . . . . 5
43exbii 1712 . . . 4
52, 4bitr3i 254 . . 3
6 abbi 2553 . . 3
75, 6xchnxbi 309 . 2
81, 7bitr2i 253 1
 Colors of variables: wff setvar class Syntax hints:   wn 3   wb 187  wal 1435   wceq 1437  wex 1659  cab 2407   wne 2618 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1665  ax-4 1678  ax-5 1748  ax-6 1794  ax-7 1839  ax-10 1887  ax-11 1892  ax-12 1905  ax-13 2053  ax-ext 2400 This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-sb 1787  df-clab 2408  df-cleq 2414  df-clel 2417  df-ne 2620 This theorem is referenced by:  suppvalbr  6925
 Copyright terms: Public domain W3C validator