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| Description: The (strong) Goldbach partition of 9. (Contributed by AV, 26-Jul-2020.) | 
| Ref | Expression | 
|---|---|
| gbpart9 | ⊢ 9 = ((3 + 3) + 3) | 
| Step | Hyp | Ref | Expression | 
|---|---|---|---|
| 1 | 3p3e6 12418 | . . 3 ⊢ (3 + 3) = 6 | |
| 2 | 1 | oveq1i 7441 | . 2 ⊢ ((3 + 3) + 3) = (6 + 3) | 
| 3 | 6p3e9 12426 | . 2 ⊢ (6 + 3) = 9 | |
| 4 | 2, 3 | eqtr2i 2766 | 1 ⊢ 9 = ((3 + 3) + 3) | 
| Colors of variables: wff setvar class | 
| Syntax hints: = wceq 1540 (class class class)co 7431 + caddc 11158 3c3 12322 6c6 12325 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: 9gbo 47761 | 
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