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Mirrors > Home > MPE Home > Th. List > 4p4e8 | Structured version Visualization version GIF version |
Description: 4 + 4 = 8. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
4p4e8 | ⊢ (4 + 4) = 8 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-4 12284 | . . . 4 ⊢ 4 = (3 + 1) | |
2 | 1 | oveq2i 7423 | . . 3 ⊢ (4 + 4) = (4 + (3 + 1)) |
3 | 4cn 12304 | . . . 4 ⊢ 4 ∈ ℂ | |
4 | 3cn 12300 | . . . 4 ⊢ 3 ∈ ℂ | |
5 | ax-1cn 11174 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 11231 | . . 3 ⊢ ((4 + 3) + 1) = (4 + (3 + 1)) |
7 | 2, 6 | eqtr4i 2762 | . 2 ⊢ (4 + 4) = ((4 + 3) + 1) |
8 | df-8 12288 | . . 3 ⊢ 8 = (7 + 1) | |
9 | 4p3e7 12373 | . . . 4 ⊢ (4 + 3) = 7 | |
10 | 9 | oveq1i 7422 | . . 3 ⊢ ((4 + 3) + 1) = (7 + 1) |
11 | 8, 10 | eqtr4i 2762 | . 2 ⊢ 8 = ((4 + 3) + 1) |
12 | 7, 11 | eqtr4i 2762 | 1 ⊢ (4 + 4) = 8 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1540 (class class class)co 7412 1c1 11117 + caddc 11119 3c3 12275 4c4 12276 7c7 12279 8c8 12280 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1796 ax-4 1810 ax-5 1912 ax-6 1970 ax-7 2010 ax-8 2107 ax-9 2115 ax-ext 2702 ax-1cn 11174 ax-addcl 11176 ax-addass 11181 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 845 df-3an 1088 df-tru 1543 df-fal 1553 df-ex 1781 df-sb 2067 df-clab 2709 df-cleq 2723 df-clel 2809 df-rab 3432 df-v 3475 df-dif 3951 df-un 3953 df-in 3955 df-ss 3965 df-nul 4323 df-if 4529 df-sn 4629 df-pr 4631 df-op 4635 df-uni 4909 df-br 5149 df-iota 6495 df-fv 6551 df-ov 7415 df-2 12282 df-3 12283 df-4 12284 df-5 12285 df-6 12286 df-7 12287 df-8 12288 |
This theorem is referenced by: 4t2e8 12387 83prm 17063 1259lem2 17072 1259lem3 17073 2503lem2 17078 4001lem2 17082 quart1lem 26701 log2ub 26795 hgt750lem2 34128 3exp7 41385 3lexlogpow5ineq1 41386 3cubeslem3r 41888 |
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