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Theorem axext2 2418
 Description: The Axiom of Extensionality (ax-ext 2417) 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 2417 . 2
2 19.36v 1919 . 2
31, 2mpbir 201 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549  wex 1550 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1555  ax-5 1566  ax-17 1626  ax-9 1666  ax-8 1687  ax-6 1744  ax-11 1761  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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