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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 2164 | . 2 | |
2 | nfsab1 2160 | . . . 4 | |
3 | nfsab1 2160 | . . . 4 | |
4 | 2, 3 | nfbi 1582 | . . 3 |
5 | nfv 1521 | . . 3 | |
6 | df-clab 2157 | . . . . 5 | |
7 | sbequ12r 1765 | . . . . 5 | |
8 | 6, 7 | syl5bb 191 | . . . 4 |
9 | df-clab 2157 | . . . . 5 | |
10 | sbequ12r 1765 | . . . . 5 | |
11 | 9, 10 | syl5bb 191 | . . . 4 |
12 | 8, 11 | bibi12d 234 | . . 3 |
13 | 4, 5, 12 | cbval 1747 | . 2 |
14 | 1, 13 | bitr2i 184 | 1 |
Colors of variables: wff set class |
Syntax hints: wb 104 wal 1346 wceq 1348 wsb 1755 wcel 2141 cab 2156 |
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 1440 ax-7 1441 ax-gen 1442 ax-ie1 1486 ax-ie2 1487 ax-8 1497 ax-11 1499 ax-4 1503 ax-17 1519 ax-i9 1523 ax-ial 1527 ax-i5r 1528 ax-ext 2152 |
This theorem depends on definitions: df-bi 116 df-tru 1351 df-nf 1454 df-sb 1756 df-clab 2157 df-cleq 2163 |
This theorem is referenced by: abbii 2286 abbid 2287 rabbi 2647 sbcbi2 3005 dfiota2 5159 iotabi 5167 uniabio 5168 |
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