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

Theorem sbcbig 2921
 Description: Distribution of class substitution over biconditional. (Contributed by Raph Levien, 10-Apr-2004.)
Assertion
Ref Expression
sbcbig

Proof of Theorem sbcbig
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfsbcq2 2879 . 2
2 dfsbcq2 2879 . . 3
3 dfsbcq2 2879 . . 3
42, 3bibi12d 234 . 2
5 sbbi 1906 . 2
61, 4, 5vtoclbg 2716 1
 Colors of variables: wff set class Syntax hints:   wi 4   wb 104   wceq 1312   wcel 1461  wsb 1716  wsbc 2876 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-io 681  ax-5 1404  ax-7 1405  ax-gen 1406  ax-ie1 1450  ax-ie2 1451  ax-8 1463  ax-10 1464  ax-11 1465  ax-i12 1466  ax-bndl 1467  ax-4 1468  ax-17 1487  ax-i9 1491  ax-ial 1495  ax-i5r 1496  ax-ext 2095 This theorem depends on definitions:  df-bi 116  df-tru 1315  df-nf 1418  df-sb 1717  df-clab 2100  df-cleq 2106  df-clel 2109  df-nfc 2242  df-v 2657  df-sbc 2877 This theorem is referenced by:  sbcbi1  2924  sbcabel  2956
 Copyright terms: Public domain W3C validator