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Mirrors > Home > MPE Home > Th. List > cbvoprab2 | Structured version Visualization version Unicode version |
Description: Change the second bound variable in an operation abstraction. (Contributed by Jeff Madsen, 11-Jun-2010.) (Revised by Mario Carneiro, 11-Dec-2016.) |
Ref | Expression |
---|---|
cbvoprab2.1 |
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cbvoprab2.2 |
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cbvoprab2.3 |
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Ref | Expression |
---|---|
cbvoprab2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | nfv 1769 |
. . . . . . 7
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2 | cbvoprab2.1 |
. . . . . . 7
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3 | 1, 2 | nfan 2031 |
. . . . . 6
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4 | 3 | nfex 2050 |
. . . . 5
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5 | nfv 1769 |
. . . . . . 7
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6 | cbvoprab2.2 |
. . . . . . 7
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7 | 5, 6 | nfan 2031 |
. . . . . 6
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8 | 7 | nfex 2050 |
. . . . 5
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9 | opeq2 4159 |
. . . . . . . . 9
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10 | 9 | opeq1d 4164 |
. . . . . . . 8
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11 | 10 | eqeq2d 2481 |
. . . . . . 7
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12 | cbvoprab2.3 |
. . . . . . 7
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13 | 11, 12 | anbi12d 725 |
. . . . . 6
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14 | 13 | exbidv 1776 |
. . . . 5
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15 | 4, 8, 14 | cbvex 2128 |
. . . 4
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16 | 15 | exbii 1726 |
. . 3
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17 | 16 | abbii 2587 |
. 2
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18 | df-oprab 6312 |
. 2
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19 | df-oprab 6312 |
. 2
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20 | 17, 18, 19 | 3eqtr4i 2503 |
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 1677 ax-4 1690 ax-5 1766 ax-6 1813 ax-7 1859 ax-10 1932 ax-11 1937 ax-12 1950 ax-13 2104 ax-ext 2451 |
This theorem depends on definitions: df-bi 190 df-or 377 df-an 378 df-3an 1009 df-tru 1455 df-ex 1672 df-nf 1676 df-sb 1806 df-clab 2458 df-cleq 2464 df-clel 2467 df-nfc 2601 df-rab 2765 df-v 3033 df-dif 3393 df-un 3395 df-in 3397 df-ss 3404 df-nul 3723 df-if 3873 df-sn 3960 df-pr 3962 df-op 3966 df-oprab 6312 |
This theorem is referenced by: (None) |
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