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Theorem axext3 2279
 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 1701 . . . . 5
21bibi1d 310 . . . 4
32albidv 1615 . . 3
4 equequ1 1667 . . 3
53, 4imbi12d 311 . 2
6 ax-ext 2277 . 2
75, 6chvarv 1966 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 176  wal 1530   wceq 1632   wcel 1696 This theorem is referenced by:  axext4  2280  axextnd  8229  axextdist  24227 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-14 1700  ax-6 1715  ax-7 1720  ax-11 1727  ax-12 1878  ax-ext 2277 This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1310  df-ex 1532  df-nf 1535
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