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Theorem axext3 2336
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 1715 . . . . 5
21bibi1d 310 . . . 4
32albidv 1625 . . 3
4 equequ1 1684 . . 3
53, 4imbi12d 311 . 2
6 ax-ext 2334 . 2
75, 6chvarv 2013 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 176  wal 1540   wceq 1642   wcel 1710
This theorem is referenced by:  axext4  2337
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-14 1714  ax-6 1729  ax-7 1734  ax-11 1746  ax-12 1925  ax-ext 2334
This theorem depends on definitions:  df-bi 177  df-an 360  df-tru 1319  df-ex 1542  df-nf 1545
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