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Mirrors > Home > ILE Home > Th. List > ralab2 | Unicode version |
Description: Universal quantification over a class abstraction. (Contributed by Mario Carneiro, 3-Sep-2015.) |
Ref | Expression |
---|---|
ralab2.1 |
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Ref | Expression |
---|---|
ralab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2422 |
. 2
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2 | nfsab1 2130 |
. . . 4
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3 | nfv 1509 |
. . . 4
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4 | 2, 3 | nfim 1552 |
. . 3
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5 | nfv 1509 |
. . 3
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6 | eleq1 2203 |
. . . . 5
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7 | abid 2128 |
. . . . 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 | imbi12d 233 |
. . 3
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11 | 4, 5, 10 | cbval 1728 |
. 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-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-nf 1438 df-sb 1737 df-clab 2127 df-cleq 2133 df-clel 2136 df-ral 2422 |
This theorem is referenced by: ralrab2 2853 ssintab 3796 |
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