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Mirrors > Home > MPE Home > Th. List > 6p3e9 | Structured version Visualization version GIF version |
Description: 6 + 3 = 9. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
6p3e9 | ⊢ (6 + 3) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-3 12213 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 7364 | . . 3 ⊢ (6 + 3) = (6 + (2 + 1)) |
3 | 6cn 12240 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 2cn 12224 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 11105 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 11161 | . . 3 ⊢ ((6 + 2) + 1) = (6 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2767 | . 2 ⊢ (6 + 3) = ((6 + 2) + 1) |
8 | df-9 12219 | . . 3 ⊢ 9 = (8 + 1) | |
9 | 6p2e8 12308 | . . . 4 ⊢ (6 + 2) = 8 | |
10 | 9 | oveq1i 7363 | . . 3 ⊢ ((6 + 2) + 1) = (8 + 1) |
11 | 8, 10 | eqtr4i 2767 | . 2 ⊢ 9 = ((6 + 2) + 1) |
12 | 7, 11 | eqtr4i 2767 | 1 ⊢ (6 + 3) = 9 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 (class class class)co 7353 1c1 11048 + caddc 11050 2c2 12204 3c3 12205 6c6 12208 8c8 12210 9c9 12211 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2707 ax-1cn 11105 ax-addcl 11107 ax-addass 11112 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2714 df-cleq 2728 df-clel 2814 df-rab 3406 df-v 3445 df-dif 3911 df-un 3913 df-in 3915 df-ss 3925 df-nul 4281 df-if 4485 df-sn 4585 df-pr 4587 df-op 4591 df-uni 4864 df-br 5104 df-iota 6445 df-fv 6501 df-ov 7356 df-2 12212 df-3 12213 df-4 12214 df-5 12215 df-6 12216 df-7 12217 df-8 12218 df-9 12219 |
This theorem is referenced by: 3t3e9 12316 6p4e10 12686 2exp8 16953 139prm 16988 2503lem2 17002 4001lem1 17005 4001lem2 17006 4001lem4 17008 log2ublem3 26282 ex-gcd 29287 hgt750lem2 33134 kur14lem8 33676 problem5 34126 fmtno5lem1 45677 139prmALT 45720 gboge9 45888 gbpart9 45893 nnsum4primeseven 45924 |
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