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Theorem abbi 2151
 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 2034 . 2
2 nfsab1 2030 . . . 4
3 nfsab1 2030 . . . 4
42, 3nfbi 1481 . . 3
5 nfv 1421 . . 3
6 df-clab 2027 . . . . 5
7 sbequ12r 1655 . . . . 5
86, 7syl5bb 181 . . . 4
9 df-clab 2027 . . . . 5
10 sbequ12r 1655 . . . . 5
119, 10syl5bb 181 . . . 4
128, 11bibi12d 224 . . 3
134, 5, 12cbval 1637 . 2
141, 13bitr2i 174 1
 Colors of variables: wff set class Syntax hints:   wb 98  wal 1241   wceq 1243   wcel 1393  wsb 1645  cab 2026 This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-ia2 100  ax-ia3 101  ax-5 1336  ax-7 1337  ax-gen 1338  ax-ie1 1382  ax-ie2 1383  ax-8 1395  ax-11 1397  ax-4 1400  ax-17 1419  ax-i9 1423  ax-ial 1427  ax-i5r 1428  ax-ext 2022 This theorem depends on definitions:  df-bi 110  df-tru 1246  df-nf 1350  df-sb 1646  df-clab 2027  df-cleq 2033 This theorem is referenced by:  abbii  2153  abbid  2154  rabbi  2487  dfiota2  4868  iotabi  4876  uniabio  4877
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