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

Theorem sbeqalb 2933
 Description: Theorem *14.121 in [WhiteheadRussell] p. 185. (Contributed by Andrew Salmon, 28-Jun-2011.) (Proof shortened by Wolf Lammen, 9-May-2013.)
Assertion
Ref Expression
sbeqalb
Distinct variable groups:   ,   ,
Allowed substitution hints:   ()   ()

Proof of Theorem sbeqalb
StepHypRef Expression
1 bibi1 239 . . . . 5
21biimpa 292 . . . 4
32biimpd 143 . . 3
43alanimi 1418 . 2
5 sbceqal 2932 . 2
64, 5syl5 32 1
 Colors of variables: wff set class Syntax hints:   wi 4   wa 103   wb 104  wal 1312   wceq 1314   wcel 1463 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 1406  ax-7 1407  ax-gen 1408  ax-ie1 1452  ax-ie2 1453  ax-8 1465  ax-10 1466  ax-11 1467  ax-i12 1468  ax-bndl 1469  ax-4 1470  ax-17 1489  ax-i9 1493  ax-ial 1497  ax-i5r 1498  ax-ext 2097 This theorem depends on definitions:  df-bi 116  df-tru 1317  df-nf 1420  df-sb 1719  df-clab 2102  df-cleq 2108  df-clel 2111  df-nfc 2244  df-v 2659  df-sbc 2879 This theorem is referenced by:  iotaval  5057
 Copyright terms: Public domain W3C validator