Intuitionistic Logic Explorer < Previous   Next > Nearby theorems Mirrors  >  Home  >  ILE Home  >  Th. List  >  2sb5rf Unicode version

Theorem 2sb5rf 1865
 Description: Reversed double substitution. (Contributed by NM, 3-Feb-2005.)
Hypotheses
Ref Expression
2sb5rf.1
2sb5rf.2
Assertion
Ref Expression
2sb5rf
Distinct variable groups:   ,   ,   ,   ,
Allowed substitution hints:   (,,,)

Proof of Theorem 2sb5rf
StepHypRef Expression
1 2sb5rf.1 . . 3
21sb5rf 1732 . 2
3 19.42v 1786 . . . 4
4 sbcom2 1863 . . . . . . 7
54anbi2i 430 . . . . . 6
6 anass 381 . . . . . 6
75, 6bitri 173 . . . . 5
87exbii 1496 . . . 4
9 2sb5rf.2 . . . . . . 7
109hbsbv 1817 . . . . . 6
1110sb5rf 1732 . . . . 5
1211anbi2i 430 . . . 4
133, 8, 123bitr4ri 202 . . 3
1413exbii 1496 . 2
152, 14bitri 173 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 97   wb 98  wal 1241  wex 1381  wsb 1645 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-io 630  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-10 1396  ax-11 1397  ax-i12 1398  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428 This theorem depends on definitions:  df-bi 110  df-nf 1350  df-sb 1646 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator