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

Theorem sbcimdv 2888
 Description: Substitution analogue of Theorem 19.20 of [Margaris] p. 90 (alim 1387). (Contributed by NM, 11-Nov-2005.) (Revised by NM, 17-Aug-2018.) (Proof shortened by JJ, 7-Jul-2021.)
Hypothesis
Ref Expression
sbcimdv.1
Assertion
Ref Expression
sbcimdv
Distinct variable group:   ,
Allowed substitution hints:   ()   ()   ()

Proof of Theorem sbcimdv
StepHypRef Expression
1 sbcex 2832 . 2
2 sbcimdv.1 . . . . 5
32alrimiv 1797 . . . 4
4 spsbc 2835 . . . 4
5 sbcim1 2871 . . . 4
63, 4, 5syl56 34 . . 3
76com3l 80 . 2
81, 7mpdi 42 1
 Colors of variables: wff set class Syntax hints:   wi 4  wal 1283   wcel 1434  cvv 2610  wsbc 2824 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-io 663  ax-5 1377  ax-7 1378  ax-gen 1379  ax-ie1 1423  ax-ie2 1424  ax-8 1436  ax-10 1437  ax-11 1438  ax-i12 1439  ax-bndl 1440  ax-4 1441  ax-17 1460  ax-i9 1464  ax-ial 1468  ax-i5r 1469  ax-ext 2065 This theorem depends on definitions:  df-bi 115  df-tru 1288  df-nf 1391  df-sb 1688  df-clab 2070  df-cleq 2076  df-clel 2079  df-nfc 2212  df-v 2612  df-sbc 2825 This theorem is referenced by: (None)
 Copyright terms: Public domain W3C validator