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Mathbox for Norm Megill |
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Mirrors > Home > MPE Home > Th. List > Mathboxes > paddssat | Structured version Visualization version Unicode version |
Description: A projective subspace sum is a set of atoms. (Contributed by NM, 3-Jan-2012.) |
Ref | Expression |
---|---|
padd0.a |
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padd0.p |
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Ref | Expression |
---|---|
paddssat |
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Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2451 |
. . 3
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2 | eqid 2451 |
. . 3
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3 | padd0.a |
. . 3
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4 | padd0.p |
. . 3
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5 | 1, 2, 3, 4 | paddval 33363 |
. 2
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6 | unss 3608 |
. . . . . 6
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7 | 6 | biimpi 198 |
. . . . 5
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8 | ssrab2 3514 |
. . . . 5
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9 | 7, 8 | jctir 541 |
. . . 4
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10 | unss 3608 |
. . . 4
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11 | 9, 10 | sylib 200 |
. . 3
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12 | 11 | 3adant1 1026 |
. 2
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13 | 5, 12 | eqsstrd 3466 |
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 1669 ax-4 1682 ax-5 1758 ax-6 1805 ax-7 1851 ax-8 1889 ax-9 1896 ax-10 1915 ax-11 1920 ax-12 1933 ax-13 2091 ax-ext 2431 ax-rep 4515 ax-sep 4525 ax-nul 4534 ax-pow 4581 ax-pr 4639 ax-un 6583 |
This theorem depends on definitions: df-bi 189 df-or 372 df-an 373 df-3an 987 df-tru 1447 df-ex 1664 df-nf 1668 df-sb 1798 df-eu 2303 df-mo 2304 df-clab 2438 df-cleq 2444 df-clel 2447 df-nfc 2581 df-ne 2624 df-ral 2742 df-rex 2743 df-reu 2744 df-rab 2746 df-v 3047 df-sbc 3268 df-csb 3364 df-dif 3407 df-un 3409 df-in 3411 df-ss 3418 df-nul 3732 df-if 3882 df-pw 3953 df-sn 3969 df-pr 3971 df-op 3975 df-uni 4199 df-iun 4280 df-br 4403 df-opab 4462 df-mpt 4463 df-id 4749 df-xp 4840 df-rel 4841 df-cnv 4842 df-co 4843 df-dm 4844 df-rn 4845 df-res 4846 df-ima 4847 df-iota 5546 df-fun 5584 df-fn 5585 df-f 5586 df-f1 5587 df-fo 5588 df-f1o 5589 df-fv 5590 df-ov 6293 df-oprab 6294 df-mpt2 6295 df-1st 6793 df-2nd 6794 df-padd 33361 |
This theorem is referenced by: paddasslem8 33392 paddasslem11 33395 paddasslem12 33396 paddasslem13 33397 paddasslem16 33400 paddasslem17 33401 paddass 33403 padd4N 33405 paddclN 33407 pmodl42N 33416 pclunN 33463 paddunN 33492 pmapocjN 33495 pclfinclN 33515 osumcllem1N 33521 osumcllem2N 33522 osumcllem9N 33529 osumcllem11N 33531 osumclN 33532 pexmidlem6N 33540 pexmidlem8N 33542 pl42lem3N 33546 |
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