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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 12328 | . . . 4 ⊢ 3 = (2 + 1) | |
2 | 1 | oveq2i 7442 | . . 3 ⊢ (6 + 3) = (6 + (2 + 1)) |
3 | 6cn 12355 | . . . 4 ⊢ 6 ∈ ℂ | |
4 | 2cn 12339 | . . . 4 ⊢ 2 ∈ ℂ | |
5 | ax-1cn 11211 | . . . 4 ⊢ 1 ∈ ℂ | |
6 | 3, 4, 5 | addassi 11269 | . . 3 ⊢ ((6 + 2) + 1) = (6 + (2 + 1)) |
7 | 2, 6 | eqtr4i 2766 | . 2 ⊢ (6 + 3) = ((6 + 2) + 1) |
8 | df-9 12334 | . . 3 ⊢ 9 = (8 + 1) | |
9 | 6p2e8 12423 | . . . 4 ⊢ (6 + 2) = 8 | |
10 | 9 | oveq1i 7441 | . . 3 ⊢ ((6 + 2) + 1) = (8 + 1) |
11 | 8, 10 | eqtr4i 2766 | . 2 ⊢ 9 = ((6 + 2) + 1) |
12 | 7, 11 | eqtr4i 2766 | 1 ⊢ (6 + 3) = 9 |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1537 (class class class)co 7431 1c1 11154 + caddc 11156 2c2 12319 3c3 12320 6c6 12323 8c8 12325 9c9 12326 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1792 ax-4 1806 ax-5 1908 ax-6 1965 ax-7 2005 ax-8 2108 ax-9 2116 ax-ext 2706 ax-1cn 11211 ax-addcl 11213 ax-addass 11218 |
This theorem depends on definitions: df-bi 207 df-an 396 df-or 848 df-3an 1088 df-tru 1540 df-fal 1550 df-ex 1777 df-sb 2063 df-clab 2713 df-cleq 2727 df-clel 2814 df-rab 3434 df-v 3480 df-dif 3966 df-un 3968 df-ss 3980 df-nul 4340 df-if 4532 df-sn 4632 df-pr 4634 df-op 4638 df-uni 4913 df-br 5149 df-iota 6516 df-fv 6571 df-ov 7434 df-2 12327 df-3 12328 df-4 12329 df-5 12330 df-6 12331 df-7 12332 df-8 12333 df-9 12334 |
This theorem is referenced by: 3t3e9 12431 6p4e10 12803 2exp8 17123 139prm 17158 2503lem2 17172 4001lem1 17175 4001lem2 17176 4001lem4 17178 log2ublem3 27006 ex-gcd 30486 hgt750lem2 34646 kur14lem8 35198 problem5 35654 fmtno5lem1 47478 139prmALT 47521 gboge9 47689 gbpart9 47694 nnsum4primeseven 47725 |
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