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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 12329 | . . . . 5 ⊢ 2 = (1 + 1) | |
| 2 | 1 | oveq2i 7442 | . . . 4 ⊢ (7 + 2) = (7 + (1 + 1)) |
| 3 | 7cn 12360 | . . . . 5 ⊢ 7 ∈ ℂ | |
| 4 | ax-1cn 11213 | . . . . 5 ⊢ 1 ∈ ℂ | |
| 5 | 3, 4, 4 | addassi 11271 | . . . 4 ⊢ ((7 + 1) + 1) = (7 + (1 + 1)) |
| 6 | 2, 5 | eqtr4i 2768 | . . 3 ⊢ (7 + 2) = ((7 + 1) + 1) |
| 7 | df-8 12335 | . . . 4 ⊢ 8 = (7 + 1) | |
| 8 | 7 | oveq1i 7441 | . . 3 ⊢ (8 + 1) = ((7 + 1) + 1) |
| 9 | 6, 8 | eqtr4i 2768 | . 2 ⊢ (7 + 2) = (8 + 1) |
| 10 | df-9 12336 | . 2 ⊢ 9 = (8 + 1) | |
| 11 | 9, 10 | eqtr4i 2768 | 1 ⊢ (7 + 2) = 9 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 1c1 11156 + caddc 11158 2c2 12321 7c7 12326 8c8 12327 9c9 12328 |
| This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1795 ax-4 1809 ax-5 1910 ax-6 1967 ax-7 2007 ax-8 2110 ax-9 2118 ax-ext 2708 ax-1cn 11213 ax-addcl 11215 ax-addass 11220 |
| This theorem depends on definitions: df-bi 207 df-an 396 df-or 849 df-3an 1089 df-tru 1543 df-fal 1553 df-ex 1780 df-sb 2065 df-clab 2715 df-cleq 2729 df-clel 2816 df-rab 3437 df-v 3482 df-dif 3954 df-un 3956 df-ss 3968 df-nul 4334 df-if 4526 df-sn 4627 df-pr 4629 df-op 4633 df-uni 4908 df-br 5144 df-iota 6514 df-fv 6569 df-ov 7434 df-2 12329 df-3 12330 df-4 12331 df-5 12332 df-6 12333 df-7 12334 df-8 12335 df-9 12336 |
| This theorem is referenced by: 7p3e10 12808 7t7e49 12847 cos2bnd 16224 prmlem2 17157 139prm 17161 1259lem2 17169 1259lem3 17170 1259lem4 17171 1259lem5 17172 2503lem2 17175 4001lem4 17181 hgt750lem2 34667 aks4d1p1p7 42075 fmtno5lem4 47543 fmtno5fac 47569 139prmALT 47583 |
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