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Mirrors > Home > ILE Home > Th. List > rexab2 | Unicode version |
Description: Existential quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
ralab2.1 |
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Ref | Expression |
---|---|
rexab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-rex 2381 |
. 2
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2 | nfsab1 2090 |
. . . 4
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3 | nfv 1476 |
. . . 4
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4 | 2, 3 | nfan 1512 |
. . 3
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5 | nfv 1476 |
. . 3
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6 | eleq1 2162 |
. . . . 5
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7 | abid 2088 |
. . . . 5
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8 | 6, 7 | syl6bb 195 |
. . . 4
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9 | ralab2.1 |
. . . 4
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10 | 8, 9 | anbi12d 460 |
. . 3
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11 | 4, 5, 10 | cbvex 1697 |
. 2
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12 | 1, 11 | bitri 183 |
1
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Colors of variables: wff set class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 105 ax-ia2 106 ax-ia3 107 ax-5 1391 ax-7 1392 ax-gen 1393 ax-ie1 1437 ax-ie2 1438 ax-8 1450 ax-11 1452 ax-4 1455 ax-17 1474 ax-i9 1478 ax-ial 1482 ax-ext 2082 |
This theorem depends on definitions: df-bi 116 df-nf 1405 df-sb 1704 df-clab 2087 df-cleq 2093 df-clel 2096 df-rex 2381 |
This theorem is referenced by: rexrab2 2804 |
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