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Theorem axext3 2419
 Description: A generalization of the Axiom of Extensionality in which and need not be distinct. (Contributed by NM, 15-Sep-1993.) (Proof shortened by Andrew Salmon, 12-Aug-2011.)
Assertion
Ref Expression
axext3
Distinct variable groups:   ,   ,

Proof of Theorem axext3
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 elequ2 1730 . . . . 5
21bibi1d 311 . . . 4
32albidv 1635 . . 3
4 equequ1 1696 . . 3
53, 4imbi12d 312 . 2
6 ax-ext 2417 . 2
75, 6chvarv 1969 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 177  wal 1549 This theorem is referenced by:  axext4  2420  axextnd  8466  axextdist  25427 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-14 1729  ax-6 1744  ax-11 1761  ax-12 1950  ax-ext 2417 This theorem depends on definitions:  df-bi 178  df-an 361  df-ex 1551  df-nf 1554
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