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Mirrors > Home > MPE Home > Th. List > Mathboxes > gbpart9 | Structured version Visualization version GIF version |
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 12348 | . . 3 ⊢ (3 + 3) = 6 | |
2 | 1 | oveq1i 7404 | . 2 ⊢ ((3 + 3) + 3) = (6 + 3) |
3 | 6p3e9 12356 | . 2 ⊢ (6 + 3) = 9 | |
4 | 2, 3 | eqtr2i 2761 | 1 ⊢ 9 = ((3 + 3) + 3) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 (class class class)co 7394 + caddc 11097 3c3 12252 6c6 12255 9c9 12258 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1797 ax-4 1811 ax-5 1913 ax-6 1971 ax-7 2011 ax-8 2108 ax-9 2116 ax-ext 2703 ax-1cn 11152 ax-addcl 11154 ax-addass 11159 |
This theorem depends on definitions: df-bi 206 df-an 397 df-or 846 df-3an 1089 df-tru 1544 df-fal 1554 df-ex 1782 df-sb 2068 df-clab 2710 df-cleq 2724 df-clel 2810 df-rab 3433 df-v 3476 df-dif 3948 df-un 3950 df-in 3952 df-ss 3962 df-nul 4320 df-if 4524 df-sn 4624 df-pr 4626 df-op 4630 df-uni 4903 df-br 5143 df-iota 6485 df-fv 6541 df-ov 7397 df-2 12259 df-3 12260 df-4 12261 df-5 12262 df-6 12263 df-7 12264 df-8 12265 df-9 12266 |
This theorem is referenced by: 9gbo 46278 |
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