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Mathbox for Thierry Arnoux |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > esumeq2 | Structured version Unicode version |
Description: Equality theorem for extended sum. (Contributed by Thierry Arnoux, 24-Dec-2016.) |
Ref | Expression |
---|---|
esumeq2 |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2451 |
. . . . 5
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2 | mpteq12 4472 |
. . . . 5
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3 | 1, 2 | mpan 670 |
. . . 4
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4 | 3 | oveq2d 6209 |
. . 3
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5 | 4 | unieqd 4202 |
. 2
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6 | df-esum 26622 |
. 2
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7 | df-esum 26622 |
. 2
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8 | 5, 6, 7 | 3eqtr4g 2517 |
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 1592 ax-4 1603 ax-5 1671 ax-6 1710 ax-7 1730 ax-10 1777 ax-11 1782 ax-12 1794 ax-13 1952 ax-ext 2430 |
This theorem depends on definitions: df-bi 185 df-or 370 df-an 371 df-3an 967 df-tru 1373 df-ex 1588 df-nf 1591 df-sb 1703 df-clab 2437 df-cleq 2443 df-clel 2446 df-nfc 2601 df-ral 2800 df-rex 2801 df-rab 2804 df-v 3073 df-dif 3432 df-un 3434 df-in 3436 df-ss 3443 df-nul 3739 df-if 3893 df-sn 3979 df-pr 3981 df-op 3985 df-uni 4193 df-br 4394 df-opab 4452 df-mpt 4453 df-iota 5482 df-fv 5527 df-ov 6196 df-esum 26622 |
This theorem is referenced by: ddemeas 26789 |
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