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Mirrors > Home > ILE Home > Th. List > abbi | Unicode version |
Description: Equivalent wff's correspond to equal class abstractions. (Contributed by NM, 25-Nov-2013.) (Revised by Mario Carneiro, 11-Aug-2016.) |
Ref | Expression |
---|---|
abbi |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | dfcleq 2034 | . 2 | |
2 | nfsab1 2030 | . . . 4 | |
3 | nfsab1 2030 | . . . 4 | |
4 | 2, 3 | nfbi 1481 | . . 3 |
5 | nfv 1421 | . . 3 | |
6 | df-clab 2027 | . . . . 5 | |
7 | sbequ12r 1655 | . . . . 5 | |
8 | 6, 7 | syl5bb 181 | . . . 4 |
9 | df-clab 2027 | . . . . 5 | |
10 | sbequ12r 1655 | . . . . 5 | |
11 | 9, 10 | syl5bb 181 | . . . 4 |
12 | 8, 11 | bibi12d 224 | . . 3 |
13 | 4, 5, 12 | cbval 1637 | . 2 |
14 | 1, 13 | bitr2i 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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