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Theorem zfcndext 9037
Description: Axiom of Extensionality ax-ext 2407, reproved from conditionless ZFC version and predicate calculus. (Contributed by NM, 15-Aug-2003.) (Proof modification is discouraged.)
Assertion
Ref Expression
zfcndext  |-  ( A. z ( z  e.  x  <->  z  e.  y )  ->  x  =  y )
Distinct variable group:    x, y, z

Proof of Theorem zfcndext
StepHypRef Expression
1 axextnd 9014 . 2  |-  E. z
( ( z  e.  x  <->  z  e.  y )  ->  x  =  y )
2119.36iv 1813 1  |-  ( A. z ( z  e.  x  <->  z  e.  y )  ->  x  =  y )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 187   A.wal 1435    = wceq 1437    e. wcel 1870
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 1751  ax-6 1797  ax-7 1841  ax-8 1872  ax-9 1874  ax-10 1889  ax-11 1894  ax-12 1907  ax-13 2055  ax-ext 2407
This theorem depends on definitions:  df-bi 188  df-an 372  df-tru 1440  df-ex 1660  df-nf 1664  df-cleq 2421  df-clel 2424  df-nfc 2579
This theorem is referenced by: (None)
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