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Mirrors > Home > MPE Home > Th. List > 6p2e8 | Structured version Visualization version GIF version |
Description: 6 + 2 = 8. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
6p2e8 | ⊢ (6 + 2) = 8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 12326 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 7441 | . . . 4 ⊢ (6 + 2) = (6 + (1 + 1)) |
3 | 6cn 12354 | . . . . 5 ⊢ 6 ∈ ℂ | |
4 | ax-1cn 11210 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 11268 | . . . 4 ⊢ ((6 + 1) + 1) = (6 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2765 | . . 3 ⊢ (6 + 2) = ((6 + 1) + 1) |
7 | df-7 12331 | . . . 4 ⊢ 7 = (6 + 1) | |
8 | 7 | oveq1i 7440 | . . 3 ⊢ (7 + 1) = ((6 + 1) + 1) |
9 | 6, 8 | eqtr4i 2765 | . 2 ⊢ (6 + 2) = (7 + 1) |
10 | df-8 12332 | . 2 ⊢ 8 = (7 + 1) | |
11 | 9, 10 | eqtr4i 2765 | 1 ⊢ (6 + 2) = 8 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1536 (class class class)co 7430 1c1 11153 + caddc 11155 2c2 12318 6c6 12322 7c7 12323 8c8 12324 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1791 ax-4 1805 ax-5 1907 ax-6 1964 ax-7 2004 ax-8 2107 ax-9 2115 ax-ext 2705 ax-1cn 11210 ax-addcl 11212 ax-addass 11217 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1539 df-fal 1549 df-ex 1776 df-sb 2062 df-clab 2712 df-cleq 2726 df-clel 2813 df-rab 3433 df-v 3479 df-dif 3965 df-un 3967 df-ss 3979 df-nul 4339 df-if 4531 df-sn 4631 df-pr 4633 df-op 4637 df-uni 4912 df-br 5148 df-iota 6515 df-fv 6570 df-ov 7433 df-2 12326 df-3 12327 df-4 12328 df-5 12329 df-6 12330 df-7 12331 df-8 12332 |
This theorem is referenced by: 6p3e9 12423 6t3e18 12835 83prm 17156 1259lem2 17165 1259lem5 17168 2503lem2 17171 2503lem3 17172 4001lem1 17174 log2ub 27006 hgt750lem2 34645 3exp7 42034 3cubeslem3l 42673 resqrtvalex 43634 imsqrtvalex 43635 lhe4.4ex1a 44324 fmtno5faclem3 47505 |
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