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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 11766 | . . 3 ⊢ (2 + 2) = 4 | |
2 | 1 | oveq1i 7160 | . 2 ⊢ ((2 + 2) + 3) = (4 + 3) |
3 | 4p3e7 11785 | . 2 ⊢ (4 + 3) = 7 | |
4 | 2, 3 | eqtr2i 2845 | 1 ⊢ 7 = ((2 + 2) + 3) |
Colors of variables: wff setvar class |
Syntax hints: = wceq 1533 (class class class)co 7150 + caddc 10534 2c2 11686 3c3 11687 4c4 11688 7c7 11691 |
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 1907 ax-6 1966 ax-7 2011 ax-8 2112 ax-9 2120 ax-10 2141 ax-11 2157 ax-12 2173 ax-ext 2793 ax-1cn 10589 ax-addcl 10591 ax-addass 10596 |
This theorem depends on definitions: df-bi 209 df-an 399 df-or 844 df-3an 1085 df-tru 1536 df-ex 1777 df-nf 1781 df-sb 2066 df-clab 2800 df-cleq 2814 df-clel 2893 df-nfc 2963 df-rex 3144 df-rab 3147 df-v 3496 df-dif 3938 df-un 3940 df-in 3942 df-ss 3951 df-nul 4291 df-if 4467 df-sn 4561 df-pr 4563 df-op 4567 df-uni 4832 df-br 5059 df-iota 6308 df-fv 6357 df-ov 7153 df-2 11694 df-3 11695 df-4 11696 df-5 11697 df-6 11698 df-7 11699 |
This theorem is referenced by: 7gbow 43931 |
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