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Theorem zfcndext 8991
Description: Axiom of Extensionality ax-ext 2445, 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 8966 . 2  |-  E. z
( ( z  e.  x  <->  z  e.  y )  ->  x  =  y )
2119.36aiv 1936 1  |-  ( A. z ( z  e.  x  <->  z  e.  y )  ->  x  =  y )
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    <-> wb 184   A.wal 1377    = wceq 1379    e. wcel 1767
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1601  ax-4 1612  ax-5 1680  ax-6 1719  ax-7 1739  ax-8 1769  ax-9 1771  ax-10 1786  ax-11 1791  ax-12 1803  ax-13 1968  ax-ext 2445
This theorem depends on definitions:  df-bi 185  df-an 371  df-tru 1382  df-ex 1597  df-nf 1600  df-cleq 2459  df-clel 2462  df-nfc 2617
This theorem is referenced by: (None)
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