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Mirrors > Home > MPE Home > Th. List > 7p2e9 | Structured version Visualization version GIF version |
Description: 7 + 2 = 9. (Contributed by NM, 11-May-2004.) |
Ref | Expression |
---|---|
7p2e9 | ⊢ (7 + 2) = 9 |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | df-2 11438 | . . . . 5 ⊢ 2 = (1 + 1) | |
2 | 1 | oveq2i 6933 | . . . 4 ⊢ (7 + 2) = (7 + (1 + 1)) |
3 | 7cn 11473 | . . . . 5 ⊢ 7 ∈ ℂ | |
4 | ax-1cn 10330 | . . . . 5 ⊢ 1 ∈ ℂ | |
5 | 3, 4, 4 | addassi 10387 | . . . 4 ⊢ ((7 + 1) + 1) = (7 + (1 + 1)) |
6 | 2, 5 | eqtr4i 2805 | . . 3 ⊢ (7 + 2) = ((7 + 1) + 1) |
7 | df-8 11444 | . . . 4 ⊢ 8 = (7 + 1) | |
8 | 7 | oveq1i 6932 | . . 3 ⊢ (8 + 1) = ((7 + 1) + 1) |
9 | 6, 8 | eqtr4i 2805 | . 2 ⊢ (7 + 2) = (8 + 1) |
10 | df-9 11445 | . 2 ⊢ 9 = (8 + 1) | |
11 | 9, 10 | eqtr4i 2805 | 1 ⊢ (7 + 2) = 9 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1601 (class class class)co 6922 1c1 10273 + caddc 10275 2c2 11430 7c7 11435 8c8 11436 9c9 11437 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1839 ax-4 1853 ax-5 1953 ax-6 2021 ax-7 2055 ax-9 2116 ax-10 2135 ax-11 2150 ax-12 2163 ax-13 2334 ax-ext 2754 ax-1cn 10330 ax-addcl 10332 ax-addass 10337 |
This theorem depends on definitions: df-bi 199 df-an 387 df-or 837 df-3an 1073 df-tru 1605 df-ex 1824 df-nf 1828 df-sb 2012 df-clab 2764 df-cleq 2770 df-clel 2774 df-nfc 2921 df-rex 3096 df-rab 3099 df-v 3400 df-dif 3795 df-un 3797 df-in 3799 df-ss 3806 df-nul 4142 df-if 4308 df-sn 4399 df-pr 4401 df-op 4405 df-uni 4672 df-br 4887 df-iota 6099 df-fv 6143 df-ov 6925 df-2 11438 df-3 11439 df-4 11440 df-5 11441 df-6 11442 df-7 11443 df-8 11444 df-9 11445 |
This theorem is referenced by: 7p3e10 11922 7t7e49 11961 cos2bnd 15320 prmlem2 16225 139prm 16229 1259lem2 16237 1259lem3 16238 1259lem4 16239 1259lem5 16240 2503lem2 16243 4001lem4 16249 hgt750lem2 31332 fmtno5lem4 42489 fmtno5fac 42515 139prmALT 42532 |
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