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Mirrors > Home > NFE Home > Th. List > rspc | Unicode version |
Description: Restricted specialization, using implicit substitution. (Contributed by NM, 19-Apr-2005.) (Revised by Mario Carneiro, 11-Oct-2016.) |
Ref | Expression |
---|---|
rspc.1 |
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rspc.2 |
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Ref | Expression |
---|---|
rspc |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-ral 2620 |
. 2
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2 | nfcv 2490 |
. . . 4
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3 | nfv 1619 |
. . . . 5
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4 | rspc.1 |
. . . . 5
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5 | 3, 4 | nfim 1813 |
. . . 4
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6 | eleq1 2413 |
. . . . 5
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7 | rspc.2 |
. . . . 5
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8 | 6, 7 | imbi12d 311 |
. . . 4
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9 | 2, 5, 8 | spcgf 2935 |
. . 3
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10 | 9 | pm2.43a 45 |
. 2
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11 | 1, 10 | syl5bi 208 |
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 1546 ax-5 1557 ax-17 1616 ax-9 1654 ax-8 1675 ax-6 1729 ax-7 1734 ax-11 1746 ax-12 1925 ax-ext 2334 |
This theorem depends on definitions: df-bi 177 df-or 359 df-an 360 df-tru 1319 df-ex 1542 df-nf 1545 df-sb 1649 df-clab 2340 df-cleq 2346 df-clel 2349 df-nfc 2479 df-ral 2620 df-v 2862 |
This theorem is referenced by: rspcv 2952 rspc2 2961 |
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