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Mirrors > Home > ILE Home > Th. List > oprabbid | Unicode version |
Description: Equivalent wff's yield equal operation class abstractions (deduction form). (Contributed by NM, 21-Feb-2004.) (Revised by Mario Carneiro, 24-Jun-2014.) |
Ref | Expression |
---|---|
oprabbid.1 | |
oprabbid.2 | |
oprabbid.3 | |
oprabbid.4 |
Ref | Expression |
---|---|
oprabbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oprabbid.1 | . . . 4 | |
2 | oprabbid.2 | . . . . 5 | |
3 | oprabbid.3 | . . . . . 6 | |
4 | oprabbid.4 | . . . . . . 7 | |
5 | 4 | anbi2d 461 | . . . . . 6 |
6 | 3, 5 | exbid 1609 | . . . . 5 |
7 | 2, 6 | exbid 1609 | . . . 4 |
8 | 1, 7 | exbid 1609 | . . 3 |
9 | 8 | abbidv 2288 | . 2 |
10 | df-oprab 5855 | . 2 | |
11 | df-oprab 5855 | . 2 | |
12 | 9, 10, 11 | 3eqtr4g 2228 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 103 wb 104 wceq 1348 wnf 1453 wex 1485 cab 2156 cop 3584 coprab 5852 |
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 df-oprab 5855 |
This theorem is referenced by: oprabbidv 5905 mpoeq123 5910 |
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