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Mirrors > Home > NFE Home > Th. List > cbvrexcsf | Unicode version |
Description: A more general version of cbvrexf 2831 that has no distinct variable restrictions. Changes bound variables using implicit substitution. (Contributed by Andrew Salmon, 13-Jul-2011.) (Proof shortened by Mario Carneiro, 7-Dec-2014.) |
Ref | Expression |
---|---|
cbvralcsf.1 |
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cbvralcsf.2 |
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cbvralcsf.3 |
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cbvralcsf.4 |
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cbvralcsf.5 |
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cbvralcsf.6 |
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Ref | Expression |
---|---|
cbvrexcsf |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | cbvralcsf.1 |
. . . 4
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2 | cbvralcsf.2 |
. . . 4
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3 | cbvralcsf.3 |
. . . . 5
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4 | 3 | nfn 1793 |
. . . 4
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5 | cbvralcsf.4 |
. . . . 5
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6 | 5 | nfn 1793 |
. . . 4
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7 | cbvralcsf.5 |
. . . 4
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8 | cbvralcsf.6 |
. . . . 5
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9 | 8 | notbid 285 |
. . . 4
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10 | 1, 2, 4, 6, 7, 9 | cbvralcsf 3199 |
. . 3
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11 | 10 | notbii 287 |
. 2
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12 | dfrex2 2628 |
. 2
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13 | dfrex2 2628 |
. 2
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14 | 11, 12, 13 | 3bitr4i 268 |
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-rex 2621 df-sbc 3048 df-csb 3138 |
This theorem is referenced by: cbvrexv2 3204 |
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