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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 2305 |
. 2
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2 | nfsab1 2027 |
. . . 4
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3 | nfv 1418 |
. . . 4
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4 | 2, 3 | nfim 1461 |
. . 3
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5 | nfv 1418 |
. . 3
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6 | eleq1 2097 |
. . . . 5
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7 | abid 2025 |
. . . . 5
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8 | 6, 7 | syl6bb 185 |
. . . 4
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9 | ralab2.1 |
. . . 4
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10 | 8, 9 | imbi12d 223 |
. . 3
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11 | 4, 5, 10 | cbval 1634 |
. 2
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12 | 1, 11 | bitri 173 |
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 99 ax-ia2 100 ax-ia3 101 ax-5 1333 ax-7 1334 ax-gen 1335 ax-ie1 1379 ax-ie2 1380 ax-8 1392 ax-11 1394 ax-4 1397 ax-17 1416 ax-i9 1420 ax-ial 1424 ax-i5r 1425 ax-ext 2019 |
This theorem depends on definitions: df-bi 110 df-nf 1347 df-sb 1643 df-clab 2024 df-cleq 2030 df-clel 2033 df-ral 2305 |
This theorem is referenced by: ralrab2 2700 ssintab 3623 |
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