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Theorem axext3 1879
 Description: A generalization of the Axiom of Extensionality in which and need not be distinct. (The proof was 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 1535 . . . . 5
21bibi1d 307 . . . 4
32albidv 1677 . . 3
4 equequ1 1532 . . 3
53, 4imbi12d 308 . 2
6 ax-ext 1877 . 2
75, 6chvarv 1731 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 173  wal 1322   wceq 1398   wcel 1400 This theorem is referenced by:  axext4  1880 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-5 1323  ax-6 1324  ax-gen 1326  ax-8 1402  ax-14 1407  ax-17 1413  ax-9 1424  ax-4 1429  ax-ext 1877 This theorem depends on definitions:  df-bi 174  df-ex 1328
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