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Mirrors > Home > ILE Home > Th. List > 8p2e10 | GIF version |
Description: 8 + 2 = 10. (Contributed by NM, 5-Feb-2007.) (Revised by Stanislas Polu, 7-Apr-2020.) (Revised by AV, 6-Sep-2021.) |
Ref | Expression |
---|---|
8p2e10 | ⊢ (8 + 2) = ;10 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 8980 | . . . 4 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 5888 | . . 3 ⊢ (8 + 2) = (8 + (1 + 1)) |
3 | 8cn 9007 | . . . 4 ⊢ 8 ∈ ℂ | |
4 | ax-1cn 7906 | . . . 4 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 7967 | . . 3 ⊢ ((8 + 1) + 1) = (8 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2201 | . 2 ⊢ (8 + 2) = ((8 + 1) + 1) |
7 | df-9 8987 | . . 3 ⊢ 9 = (8 + 1) | |
8 | 7 | oveq1i 5887 | . 2 ⊢ (9 + 1) = ((8 + 1) + 1) |
9 | 9p1e10 9388 | . 2 ⊢ (9 + 1) = ;10 | |
10 | 6, 8, 9 | 3eqtr2i 2204 | 1 ⊢ (8 + 2) = ;10 |
Colors of variables: wff set class |
Syntax hints: = wceq 1353 (class class class)co 5877 0cc0 7813 1c1 7814 + caddc 7816 2c2 8972 8c8 8978 9c9 8979 ;cdc 9386 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-ia1 106 ax-ia2 107 ax-ia3 108 ax-io 709 ax-5 1447 ax-7 1448 ax-gen 1449 ax-ie1 1493 ax-ie2 1494 ax-8 1504 ax-10 1505 ax-11 1506 ax-i12 1507 ax-bndl 1509 ax-4 1510 ax-17 1526 ax-i9 1530 ax-ial 1534 ax-i5r 1535 ax-ext 2159 ax-sep 4123 ax-cnex 7904 ax-resscn 7905 ax-1cn 7906 ax-1re 7907 ax-icn 7908 ax-addcl 7909 ax-addrcl 7910 ax-mulcl 7911 ax-mulcom 7914 ax-addass 7915 ax-mulass 7916 ax-distr 7917 ax-1rid 7920 ax-0id 7921 ax-cnre 7924 |
This theorem depends on definitions: df-bi 117 df-3an 980 df-tru 1356 df-nf 1461 df-sb 1763 df-clab 2164 df-cleq 2170 df-clel 2173 df-nfc 2308 df-ral 2460 df-rex 2461 df-rab 2464 df-v 2741 df-un 3135 df-in 3137 df-ss 3144 df-sn 3600 df-pr 3601 df-op 3603 df-uni 3812 df-int 3847 df-br 4006 df-iota 5180 df-fv 5226 df-ov 5880 df-inn 8922 df-2 8980 df-3 8981 df-4 8982 df-5 8983 df-6 8984 df-7 8985 df-8 8986 df-9 8987 df-dec 9387 |
This theorem is referenced by: 8p3e11 9466 8t5e40 9503 |
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