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

Theorem abbi 2253
 Description: Equivalent wff's correspond to equal class abstractions. (Contributed by NM, 25-Nov-2013.) (Revised by Mario Carneiro, 11-Aug-2016.)
Assertion
Ref Expression
abbi

Proof of Theorem abbi
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 dfcleq 2133 . 2
2 nfsab1 2129 . . . 4
3 nfsab1 2129 . . . 4
42, 3nfbi 1568 . . 3
5 nfv 1508 . . 3
6 df-clab 2126 . . . . 5
7 sbequ12r 1745 . . . . 5
86, 7syl5bb 191 . . . 4
9 df-clab 2126 . . . . 5
10 sbequ12r 1745 . . . . 5
119, 10syl5bb 191 . . . 4
128, 11bibi12d 234 . . 3
134, 5, 12cbval 1727 . 2
141, 13bitr2i 184 1
 Colors of variables: wff set class Syntax hints:   wb 104  wal 1329   wceq 1331   wcel 1480  wsb 1735  cab 2125 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-7 1424  ax-gen 1425  ax-ie1 1469  ax-ie2 1470  ax-8 1482  ax-11 1484  ax-4 1487  ax-17 1506  ax-i9 1510  ax-ial 1514  ax-i5r 1515  ax-ext 2121 This theorem depends on definitions:  df-bi 116  df-tru 1334  df-nf 1437  df-sb 1736  df-clab 2126  df-cleq 2132 This theorem is referenced by:  abbii  2255  abbid  2256  rabbi  2608  sbcbi2  2959  dfiota2  5089  iotabi  5097  uniabio  5098
 Copyright terms: Public domain W3C validator