ILE Home Intuitionistic Logic Explorer < Previous   Next >
Nearby theorems
Mirrors  >  Home  >  ILE Home  >  Th. List  >  axext3 Structured version   Unicode version

Theorem axext3 2020
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 1598 . . . . 5
21bibi1d 222 . . . 4
32albidv 1702 . . 3
4 equequ1 1595 . . 3
53, 4imbi12d 223 . 2
6 ax-ext 2019 . 2
75, 6chvarv 1809 1
Colors of variables: wff set class
Syntax hints:   wi 4   wb 98  wal 1240
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1333  ax-gen 1335  ax-ie1 1379  ax-ie2 1380  ax-8 1392  ax-4 1397  ax-14 1402  ax-17 1416  ax-i9 1420  ax-ial 1424  ax-ext 2019
This theorem depends on definitions:  df-bi 110  df-nf 1347
This theorem is referenced by:  axext4  2021
  Copyright terms: Public domain W3C validator