![]() |
Metamath Proof Explorer |
< Previous
Next >
Nearby theorems |
|
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 11292 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 6825 | . . 3 ⊢ (3 + 3) = (3 + (2 + 1)) |
3 | 3cn 11307 | . . . 4 ⊢ 3 ∈ ℂ | |
4 | 2cn 11303 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 10206 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 10260 | . . 3 ⊢ ((3 + 2) + 1) = (3 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2785 | . 2 ⊢ (3 + 3) = ((3 + 2) + 1) |
8 | df-6 11295 | . . 3 ⊢ 6 = (5 + 1) | |
9 | 3p2e5 11372 | . . . 4 ⊢ (3 + 2) = 5 | |
10 | 9 | oveq1i 6824 | . . 3 ⊢ ((3 + 2) + 1) = (5 + 1) |
11 | 8, 10 | eqtr4i 2785 | . 2 ⊢ 6 = ((3 + 2) + 1) |
12 | 7, 11 | eqtr4i 2785 | 1 ⊢ (3 + 3) = 6 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1632 (class class class)co 6814 1c1 10149 + caddc 10151 2c2 11282 3c3 11283 5c5 11285 6c6 11286 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1871 ax-4 1886 ax-5 1988 ax-6 2054 ax-7 2090 ax-9 2148 ax-10 2168 ax-11 2183 ax-12 2196 ax-13 2391 ax-ext 2740 ax-resscn 10205 ax-1cn 10206 ax-icn 10207 ax-addcl 10208 ax-addrcl 10209 ax-mulcl 10210 ax-mulrcl 10211 ax-addass 10213 ax-i2m1 10216 ax-1ne0 10217 ax-rrecex 10220 ax-cnre 10221 |
This theorem depends on definitions: df-bi 197 df-or 384 df-an 385 df-3an 1074 df-tru 1635 df-ex 1854 df-nf 1859 df-sb 2047 df-clab 2747 df-cleq 2753 df-clel 2756 df-nfc 2891 df-ne 2933 df-ral 3055 df-rex 3056 df-rab 3059 df-v 3342 df-dif 3718 df-un 3720 df-in 3722 df-ss 3729 df-nul 4059 df-if 4231 df-sn 4322 df-pr 4324 df-op 4328 df-uni 4589 df-br 4805 df-iota 6012 df-fv 6057 df-ov 6817 df-2 11291 df-3 11292 df-4 11293 df-5 11294 df-6 11295 |
This theorem is referenced by: 3t2e6 11391 163prm 16054 631prm 16056 2503prm 16069 binom4 24797 ex-dvds 27645 ex-gcd 27646 kur14lem8 31523 gbegt5 42177 gboge9 42180 gbpart6 42182 gbpart9 42185 gbpart11 42186 zlmodzxzequa 42813 |
Copyright terms: Public domain | W3C validator |