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Theorem axext2 2335
Description: The Axiom of Extensionality (ax-ext 2334) 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 2334 . 2
2 19.36v 1896 . 2
31, 2mpbir 200 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 176  wal 1540  wex 1541   wceq 1642   wcel 1710
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1546  ax-5 1557  ax-17 1616  ax-9 1654  ax-8 1675  ax-6 1729  ax-11 1746  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-ex 1542  df-nf 1545
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