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Theorem axext2 2278
 Description: The Axiom of Extensionality (ax-ext 2277) restated so that it postulates the existence of a set given two arbitrary sets and . This way to express it follows the general idea of the other ZFC axioms, which is to postulate the existence of sets given other sets. (Contributed by NM, 28-Sep-2003.)
Assertion
Ref Expression
axext2
Distinct variable group:   ,,

Proof of Theorem axext2
StepHypRef Expression
1 ax-ext 2277 . 2
2 19.36v 1849 . 2
31, 2mpbir 200 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530  wex 1531   wceq 1632   wcel 1696 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606  ax-9 1644  ax-8 1661  ax-6 1715  ax-11 1727  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1532  df-nf 1535
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