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Mathbox for Glauco Siliprandi |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > stoweidlem8 | Structured version Visualization version Unicode version |
Description: Lemma for stoweid 37919: two class variables replace two setvar variables, for the sum of two functions. (Contributed by Glauco Siliprandi, 20-Apr-2017.) |
Ref | Expression |
---|---|
stoweidlem8.1 |
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stoweidlem8.2 |
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stoweidlem8.3 |
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Ref | Expression |
---|---|
stoweidlem8 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | simp3 1009 |
. 2
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2 | eleq1 2516 |
. . . . 5
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3 | 2 | 3anbi3d 1344 |
. . . 4
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4 | stoweidlem8.3 |
. . . . . . 7
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5 | 4 | nfeq2 2606 |
. . . . . 6
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6 | fveq1 5862 |
. . . . . . . 8
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7 | 6 | oveq2d 6304 |
. . . . . . 7
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8 | 7 | adantr 467 |
. . . . . 6
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9 | 5, 8 | mpteq2da 4487 |
. . . . 5
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10 | 9 | eleq1d 2512 |
. . . 4
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11 | 3, 10 | imbi12d 322 |
. . 3
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12 | simp2 1008 |
. . . 4
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13 | eleq1 2516 |
. . . . . . 7
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14 | 13 | 3anbi2d 1343 |
. . . . . 6
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15 | stoweidlem8.2 |
. . . . . . . . 9
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16 | 15 | nfeq2 2606 |
. . . . . . . 8
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17 | fveq1 5862 |
. . . . . . . . . 10
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18 | 17 | oveq1d 6303 |
. . . . . . . . 9
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19 | 18 | adantr 467 |
. . . . . . . 8
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20 | 16, 19 | mpteq2da 4487 |
. . . . . . 7
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21 | 20 | eleq1d 2512 |
. . . . . 6
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22 | 14, 21 | imbi12d 322 |
. . . . 5
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23 | stoweidlem8.1 |
. . . . 5
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24 | 22, 23 | vtoclg 3106 |
. . . 4
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25 | 12, 24 | mpcom 37 |
. . 3
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26 | 11, 25 | vtoclg 3106 |
. 2
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27 | 1, 26 | mpcom 37 |
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 1668 ax-4 1681 ax-5 1757 ax-6 1804 ax-7 1850 ax-10 1914 ax-11 1919 ax-12 1932 ax-13 2090 ax-ext 2430 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 986 df-tru 1446 df-ex 1663 df-nf 1667 df-sb 1797 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2580 df-ral 2741 df-rex 2742 df-rab 2745 df-v 3046 df-dif 3406 df-un 3408 df-in 3410 df-ss 3417 df-nul 3731 df-if 3881 df-sn 3968 df-pr 3970 df-op 3974 df-uni 4198 df-br 4402 df-opab 4461 df-mpt 4462 df-iota 5545 df-fv 5589 df-ov 6291 |
This theorem is referenced by: stoweidlem20 37874 stoweidlem21 37875 stoweidlem22 37876 stoweidlem23 37877 |
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