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Mirrors > Home > MPE Home > Th. List > ralab2 | Structured version Visualization version 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 2742 |
. 2
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2 | nfsab1 2441 |
. . . 4
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3 | nfv 1761 |
. . . 4
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4 | 2, 3 | nfim 2003 |
. . 3
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5 | nfv 1761 |
. . 3
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6 | eleq1 2517 |
. . . . 5
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7 | abid 2439 |
. . . . 5
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8 | 6, 7 | syl6bb 265 |
. . . 4
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9 | ralab2.1 |
. . . 4
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10 | 8, 9 | imbi12d 322 |
. . 3
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11 | 4, 5, 10 | cbval 2114 |
. 2
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12 | 1, 11 | bitri 253 |
1
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Colors of variables: wff setvar class |
Syntax hints: ![]() ![]() ![]() ![]() ![]() ![]() |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 |
This theorem depends on definitions: df-bi 189 df-an 373 df-ex 1664 df-nf 1668 df-sb 1798 df-clab 2438 df-cleq 2444 df-clel 2447 df-ral 2742 |
This theorem is referenced by: ralrab2 3204 ssintab 4251 efgval 17367 efger 17368 elintabg 36180 elintima 36245 |
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