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| Mirrors > Home > MPE Home > Th. List > 5p3e8 | Structured version Visualization version GIF version | ||
| Description: 5 + 3 = 8. (Contributed by NM, 11-May-2004.) |
| Ref | Expression |
|---|---|
| 5p3e8 | ⊢ (5 + 3) = 8 |
| Step | Hyp | Ref | Expression |
|---|---|---|---|
| 1 | df-3 12330 | . . . 4 ⊢ 3 = (2 + 1) | |
| 2 | 1 | oveq2i 7442 | . . 3 ⊢ (5 + 3) = (5 + (2 + 1)) |
| 3 | 5cn 12354 | . . . 4 ⊢ 5 ∈ ℂ | |
| 4 | 2cn 12341 | . . . 4 ⊢ 2 ∈ ℂ | |
| 5 | ax-1cn 11213 | . . . 4 ⊢ 1 ∈ ℂ | |
| 6 | 3, 4, 5 | addassi 11271 | . . 3 ⊢ ((5 + 2) + 1) = (5 + (2 + 1)) |
| 7 | 2, 6 | eqtr4i 2768 | . 2 ⊢ (5 + 3) = ((5 + 2) + 1) |
| 8 | df-8 12335 | . . 3 ⊢ 8 = (7 + 1) | |
| 9 | 5p2e7 12422 | . . . 4 ⊢ (5 + 2) = 7 | |
| 10 | 9 | oveq1i 7441 | . . 3 ⊢ ((5 + 2) + 1) = (7 + 1) |
| 11 | 8, 10 | eqtr4i 2768 | . 2 ⊢ 8 = ((5 + 2) + 1) |
| 12 | 7, 11 | eqtr4i 2768 | 1 ⊢ (5 + 3) = 8 |
| Colors of variables: wff setvar class |
| Syntax hints: = wceq 1540 (class class class)co 7431 1c1 11156 + caddc 11158 2c2 12321 3c3 12322 5c5 12324 7c7 12326 8c8 12327 |
| 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 |
| This theorem is referenced by: 5p4e9 12424 ef01bndlem 16220 2exp16 17128 1259lem2 17169 log2ublem3 26991 log2ub 26992 bposlem8 27335 lgsdir2lem1 27369 fib6 34408 235t711 42339 ex-decpmul 42340 fmtno5lem2 47541 fmtno5lem4 47543 257prm 47548 gbpart8 47755 8gbe 47760 evengpop3 47785 ackval3012 48613 |
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