Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  sbel2x Unicode version

Theorem sbel2x 1916
 Description: Elimination of double substitution. (Contributed by NM, 5-Aug-1993.)
Assertion
Ref Expression
sbel2x
Distinct variable groups:   ,,   ,   ,,
Allowed substitution hints:   (,)

Proof of Theorem sbel2x
StepHypRef Expression
1 sbelx 1915 . . . . 5
21anbi2i 445 . . . 4
32exbii 1537 . . 3
4 sbelx 1915 . . 3
5 exdistr 1829 . . 3
63, 4, 53bitr4i 210 . 2
7 anass 393 . . 3
872exbii 1538 . 2
96, 8bitr4i 185 1
 Colors of variables: wff set class Syntax hints:   wa 102   wb 103  wex 1422  wsb 1686 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1377  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-11 1438  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468 This theorem depends on definitions:  df-bi 115  df-sb 1687 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator