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Theorem axext3 2123
 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 1692 . . . . 5
21bibi1d 232 . . . 4
32albidv 1797 . . 3
4 equequ1 1689 . . 3
53, 4imbi12d 233 . 2
6 ax-ext 2122 . 2
75, 6chvarv 1910 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104  wal 1330 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1424  ax-gen 1426  ax-ie1 1470  ax-ie2 1471  ax-8 1483  ax-4 1488  ax-14 1493  ax-17 1507  ax-i9 1511  ax-ial 1515  ax-ext 2122 This theorem depends on definitions:  df-bi 116  df-nf 1438 This theorem is referenced by:  axext4  2124
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