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Mirrors > Home > ILE Home > Th. List > 5p5e10 | Unicode version |
Description: 5 + 5 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
5p5e10 | ; |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-5 8101 | . . . 4 | |
2 | 1 | oveq2i 5543 | . . 3 |
3 | 5cn 8119 | . . . 4 | |
4 | 4cn 8117 | . . . 4 | |
5 | ax-1cn 7069 | . . . 4 | |
6 | 3, 4, 5 | addassi 7127 | . . 3 |
7 | 2, 6 | eqtr4i 2104 | . 2 |
8 | 5p4e9 8180 | . . 3 | |
9 | 8 | oveq1i 5542 | . 2 |
10 | 9p1e10 8479 | . 2 ; | |
11 | 7, 9, 10 | 3eqtri 2105 | 1 ; |
Colors of variables: wff set class |
Syntax hints: wceq 1284 (class class class)co 5532 cc0 6981 c1 6982 caddc 6984 c4 8091 c5 8092 c9 8096 ;cdc 8477 |
This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 104 ax-ia2 105 ax-ia3 106 ax-io 662 ax-5 1376 ax-7 1377 ax-gen 1378 ax-ie1 1422 ax-ie2 1423 ax-8 1435 ax-10 1436 ax-11 1437 ax-i12 1438 ax-bndl 1439 ax-4 1440 ax-17 1459 ax-i9 1463 ax-ial 1467 ax-i5r 1468 ax-ext 2063 ax-sep 3896 ax-cnex 7067 ax-resscn 7068 ax-1cn 7069 ax-1re 7070 ax-icn 7071 ax-addcl 7072 ax-addrcl 7073 ax-mulcl 7074 ax-mulcom 7077 ax-addass 7078 ax-mulass 7079 ax-distr 7080 ax-1rid 7083 ax-0id 7084 ax-cnre 7087 |
This theorem depends on definitions: df-bi 115 df-3an 921 df-tru 1287 df-nf 1390 df-sb 1686 df-clab 2068 df-cleq 2074 df-clel 2077 df-nfc 2208 df-ral 2353 df-rex 2354 df-rab 2357 df-v 2603 df-un 2977 df-in 2979 df-ss 2986 df-sn 3404 df-pr 3405 df-op 3407 df-uni 3602 df-int 3637 df-br 3786 df-iota 4887 df-fv 4930 df-ov 5535 df-inn 8040 df-2 8098 df-3 8099 df-4 8100 df-5 8101 df-6 8102 df-7 8103 df-8 8104 df-9 8105 df-dec 8478 |
This theorem is referenced by: 5t2e10 8576 5t4e20 8578 |
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