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Mirrors > Home > MPE Home > Th. List > Mathboxes > gbpart7 | Structured version Visualization version GIF version |
Description: The (weak) Goldbach partition of 7. (Contributed by AV, 20-Jul-2020.) |
Ref | Expression |
---|---|
gbpart7 | ⊢ 7 = ((2 + 2) + 3) |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | 2p2e4 12091 | . . 3 ⊢ (2 + 2) = 4 | |
2 | 1 | oveq1i 7278 | . 2 ⊢ ((2 + 2) + 3) = (4 + 3) |
3 | 4p3e7 12110 | . 2 ⊢ (4 + 3) = 7 | |
4 | 2, 3 | eqtr2i 2768 | 1 ⊢ 7 = ((2 + 2) + 3) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1541 (class class class)co 7268 + caddc 10858 2c2 12011 3c3 12012 4c4 12013 7c7 12016 |
This theorem was proved from axioms: ax-mp 5 ax-1 6 ax-2 7 ax-3 8 ax-gen 1801 ax-4 1815 ax-5 1916 ax-6 1974 ax-7 2014 ax-8 2111 ax-9 2119 ax-ext 2710 ax-1cn 10913 ax-addcl 10915 ax-addass 10920 |
This theorem depends on definitions: df-bi 206 df-an 396 df-or 844 df-3an 1087 df-tru 1544 df-fal 1554 df-ex 1786 df-sb 2071 df-clab 2717 df-cleq 2731 df-clel 2817 df-rab 3074 df-v 3432 df-dif 3894 df-un 3896 df-in 3898 df-ss 3908 df-nul 4262 df-if 4465 df-sn 4567 df-pr 4569 df-op 4573 df-uni 4845 df-br 5079 df-iota 6388 df-fv 6438 df-ov 7271 df-2 12019 df-3 12020 df-4 12021 df-5 12022 df-6 12023 df-7 12024 |
This theorem is referenced by: 7gbow 45176 |
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