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

Theorem cbvalh 1652
 Description: Rule used to change bound variables, using implicit substitition. (Contributed by NM, 5-Aug-1993.) (Proof shortened by Andrew Salmon, 25-May-2011.)
Hypotheses
Ref Expression
cbvalh.1
cbvalh.2
cbvalh.3
Assertion
Ref Expression
cbvalh

Proof of Theorem cbvalh
StepHypRef Expression
1 cbvalh.1 . . 3
2 cbvalh.2 . . 3
3 cbvalh.3 . . . 4
43biimpd 136 . . 3
51, 2, 4cbv3h 1647 . 2
63equcoms 1610 . . . 4
76biimprd 151 . . 3
82, 1, 7cbv3h 1647 . 2
95, 8impbii 121 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 102  wal 1257 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 103  ax-ia2 104  ax-ia3 105  ax-5 1352  ax-7 1353  ax-gen 1354  ax-ie1 1398  ax-ie2 1399  ax-8 1411  ax-4 1416  ax-17 1435  ax-i9 1439  ax-ial 1443 This theorem depends on definitions:  df-bi 114  df-nf 1366 This theorem is referenced by:  cbval  1653  sb8h  1750  cbvalv  1810  sb9v  1870  sb8euh  1939
 Copyright terms: Public domain W3C validator