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Mathbox for Alexander van der Vekens |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > rspceaov | Structured version Visualization version Unicode version |
Description: A frequently used special case of rspc2ev 3149 for operation values, analogous to rspceov 6347. (Contributed by Alexander van der Vekens, 26-May-2017.) |
Ref | Expression |
---|---|
rspceaov |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqidd 2472 |
. . . 4
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2 | id 22 |
. . . 4
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3 | eqidd 2472 |
. . . 4
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4 | 1, 2, 3 | aoveq123d 38825 |
. . 3
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5 | 4 | eqeq2d 2481 |
. 2
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6 | eqidd 2472 |
. . . 4
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7 | eqidd 2472 |
. . . 4
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8 | id 22 |
. . . 4
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9 | 6, 7, 8 | aoveq123d 38825 |
. . 3
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10 | 9 | eqeq2d 2481 |
. 2
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11 | 5, 10 | rspc2ev 3149 |
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-rex 2762 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-uni 4191 df-br 4396 df-opab 4455 df-xp 4845 df-rel 4846 df-cnv 4847 df-co 4848 df-dm 4849 df-res 4851 df-iota 5553 df-fun 5591 df-fv 5597 df-dfat 38762 df-afv 38763 df-aov 38764 |
This theorem is referenced by: (None) |
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