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Theorem axext2 2235
 Description: The Axiom of Extensionality (ax-ext 2234) 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 2234 . 2
2 19.36v 2029 . 2
31, 2mpbir 202 1
 Colors of variables: wff set class Syntax hints:   wi 6   wb 178  wal 1532  wex 1537   wceq 1619   wcel 1621 This theorem was proved from axioms:  ax-1 7  ax-2 8  ax-3 9  ax-mp 10  ax-5 1533  ax-6 1534  ax-gen 1536  ax-17 1628  ax-4 1692  ax-ext 2234 This theorem depends on definitions:  df-bi 179  df-an 362  df-ex 1538  df-nf 1540
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