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Mirrors > Home > ILE Home > Th. List > opabbid | Unicode version |
Description: Equivalent wff's yield equal ordered-pair class abstractions (deduction rule). (Contributed by NM, 21-Feb-2004.) (Proof shortened by Andrew Salmon, 9-Jul-2011.) |
Ref | Expression |
---|---|
opabbid.1 | |
opabbid.2 | |
opabbid.3 |
Ref | Expression |
---|---|
opabbid |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | opabbid.1 | . . . 4 | |
2 | opabbid.2 | . . . . 5 | |
3 | opabbid.3 | . . . . . 6 | |
4 | 3 | anbi2d 451 | . . . . 5 |
5 | 2, 4 | exbid 1547 | . . . 4 |
6 | 1, 5 | exbid 1547 | . . 3 |
7 | 6 | abbidv 2196 | . 2 |
8 | df-opab 3840 | . 2 | |
9 | df-opab 3840 | . 2 | |
10 | 7, 8, 9 | 3eqtr4g 2138 | 1 |
Colors of variables: wff set class |
Syntax hints: wi 4 wa 102 wb 103 wceq 1284 wnf 1389 wex 1421 cab 2067 cop 3401 copab 3838 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-11 1437 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 |
This theorem depends on definitions: df-bi 115 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-opab 3840 |
This theorem is referenced by: opabbidv 3844 mpteq12f 3858 fnoprabg 5622 |
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