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 | |
padd0.p |
Ref | Expression |
---|---|
paddssat |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | eqid 2622 | . . 3 | |
2 | eqid 2622 | . . 3 | |
3 | padd0.a | . . 3 | |
4 | padd0.p | . . 3 | |
5 | 1, 2, 3, 4 | paddval 35084 | . 2 |
6 | unss 3787 | . . . . . 6 | |
7 | 6 | biimpi 206 | . . . . 5 |
8 | ssrab2 3687 | . . . . 5 | |
9 | 7, 8 | jctir 561 | . . . 4 |
10 | unss 3787 | . . . 4 | |
11 | 9, 10 | sylib 208 | . . 3 |
12 | 11 | 3adant1 1079 | . 2 |
13 | 5, 12 | eqsstrd 3639 | 1 |
Colors of variables: wff setvar class |
Syntax hints: wi 4 wa 384 w3a 1037 wceq 1483 wcel 1990 wrex 2913 crab 2916 cun 3572 wss 3574 class class class wbr 4653 cfv 5888 (class class class)co 6650 cple 15948 cjn 16944 catm 34550 cpadd 35081 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1722 ax-4 1737 ax-5 1839 ax-6 1888 ax-7 1935 ax-8 1992 ax-9 1999 ax-10 2019 ax-11 2034 ax-12 2047 ax-13 2246 ax-ext 2602 ax-rep 4771 ax-sep 4781 ax-nul 4789 ax-pow 4843 ax-pr 4906 ax-un 6949 |
This theorem depends on definitions: df-bi 197 df-or 385 df-an 386 df-3an 1039 df-tru 1486 df-ex 1705 df-nf 1710 df-sb 1881 df-eu 2474 df-mo 2475 df-clab 2609 df-cleq 2615 df-clel 2618 df-nfc 2753 df-ne 2795 df-ral 2917 df-rex 2918 df-reu 2919 df-rab 2921 df-v 3202 df-sbc 3436 df-csb 3534 df-dif 3577 df-un 3579 df-in 3581 df-ss 3588 df-nul 3916 df-if 4087 df-pw 4160 df-sn 4178 df-pr 4180 df-op 4184 df-uni 4437 df-iun 4522 df-br 4654 df-opab 4713 df-mpt 4730 df-id 5024 df-xp 5120 df-rel 5121 df-cnv 5122 df-co 5123 df-dm 5124 df-rn 5125 df-res 5126 df-ima 5127 df-iota 5851 df-fun 5890 df-fn 5891 df-f 5892 df-f1 5893 df-fo 5894 df-f1o 5895 df-fv 5896 df-ov 6653 df-oprab 6654 df-mpt2 6655 df-1st 7168 df-2nd 7169 df-padd 35082 |
This theorem is referenced by: paddasslem8 35113 paddasslem11 35116 paddasslem12 35117 paddasslem13 35118 paddasslem16 35121 paddasslem17 35122 paddass 35124 padd4N 35126 paddclN 35128 pmodl42N 35137 pclunN 35184 paddunN 35213 pmapocjN 35216 pclfinclN 35236 osumcllem1N 35242 osumcllem2N 35243 osumcllem9N 35250 osumcllem11N 35252 osumclN 35253 pexmidlem6N 35261 pexmidlem8N 35263 pl42lem3N 35267 |
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