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Mirrors > Home > MPE Home > Th. List > 3p3e6 | Structured version Visualization version GIF version |
Description: 3 + 3 = 6. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
3p3e6 | ⊢ (3 + 3) = 6 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 11377 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 6889 | . . 3 ⊢ (3 + 3) = (3 + (2 + 1)) |
3 | 3cn 11394 | . . . 4 ⊢ 3 ∈ ℂ | |
4 | 2cn 11388 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 10282 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10339 | . . 3 ⊢ ((3 + 2) + 1) = (3 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2824 | . 2 ⊢ (3 + 3) = ((3 + 2) + 1) |
8 | df-6 11380 | . . 3 ⊢ 6 = (5 + 1) | |
9 | 3p2e5 11471 | . . . 4 ⊢ (3 + 2) = 5 | |
10 | 9 | oveq1i 6888 | . . 3 ⊢ ((3 + 2) + 1) = (5 + 1) |
11 | 8, 10 | eqtr4i 2824 | . 2 ⊢ 6 = ((3 + 2) + 1) |
12 | 7, 11 | eqtr4i 2824 | 1 ⊢ (3 + 3) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1653 (class class class)co 6878 1c1 10225 + caddc 10227 2c2 11368 3c3 11369 5c5 11371 6c6 11372 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1891 ax-4 1905 ax-5 2006 ax-6 2072 ax-7 2107 ax-9 2166 ax-10 2185 ax-11 2200 ax-12 2213 ax-13 2377 ax-ext 2777 ax-1cn 10282 ax-addcl 10284 ax-addass 10289 |
This theorem depends on definitions: df-bi 199 df-an 386 df-or 875 df-3an 1110 df-tru 1657 df-ex 1876 df-nf 1880 df-sb 2065 df-clab 2786 df-cleq 2792 df-clel 2795 df-nfc 2930 df-rex 3095 df-rab 3098 df-v 3387 df-dif 3772 df-un 3774 df-in 3776 df-ss 3783 df-nul 4116 df-if 4278 df-sn 4369 df-pr 4371 df-op 4375 df-uni 4629 df-br 4844 df-iota 6064 df-fv 6109 df-ov 6881 df-2 11376 df-3 11377 df-4 11378 df-5 11379 df-6 11380 |
This theorem is referenced by: 3t2e6 11486 163prm 16159 631prm 16161 2503prm 16174 binom4 24929 ex-dvds 27841 ex-gcd 27842 kur14lem8 31712 ex-decpmul 38003 gbegt5 42431 gboge9 42434 gbpart6 42436 gbpart9 42439 gbpart11 42440 zlmodzxzequa 43084 |
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