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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 |
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oprabbid.2 |
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oprabbid.3 |
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oprabbid.4 |
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Ref | Expression |
---|---|
oprabbid |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | oprabbid.1 |
. . . 4
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2 | oprabbid.2 |
. . . . 5
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3 | oprabbid.3 |
. . . . . 6
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4 | oprabbid.4 |
. . . . . . 7
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5 | 4 | anbi2d 460 |
. . . . . 6
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6 | 3, 5 | exbid 1596 |
. . . . 5
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7 | 2, 6 | exbid 1596 |
. . . 4
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8 | 1, 7 | exbid 1596 |
. . 3
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9 | 8 | abbidv 2258 |
. 2
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10 | df-oprab 5786 |
. 2
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11 | df-oprab 5786 |
. 2
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12 | 9, 10, 11 | 3eqtr4g 2198 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
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 1424 ax-7 1425 ax-gen 1426 ax-ie1 1470 ax-ie2 1471 ax-8 1483 ax-11 1485 ax-4 1488 ax-17 1507 ax-i9 1511 ax-ial 1515 ax-i5r 1516 ax-ext 2122 |
This theorem depends on definitions: df-bi 116 df-tru 1335 df-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-oprab 5786 |
This theorem is referenced by: oprabbidv 5833 mpoeq123 5838 |
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