Theorem gbpart7 47955

Description: The (weak) Goldbach partition of 7. (Contributed by AV, 20-Jul-2020.)

Assertion

Ref	Expression
gbpart7	⊢ 7 = ((2 + 2) + 3)

Proof of Theorem gbpart7

Step	Hyp	Ref	Expression
1		2p2e4 12273	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7366	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12292	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2758	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1541  (class class class)co 7356   + caddc 11027  2c2 12198  3c3 12199  4c4 12200  7c7 12203

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2706  ax-1cn 11082  ax-addcl 11084  ax-addass 11089

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2713  df-cleq 2726  df-clel 2809  df-rab 3398  df-v 3440  df-dif 3902  df-un 3904  df-ss 3916  df-nul 4284  df-if 4478  df-sn 4579  df-pr 4581  df-op 4585  df-uni 4862  df-br 5097  df-iota 6446  df-fv 6498  df-ov 7359  df-2 12206  df-3 12207  df-4 12208  df-5 12209  df-6 12210  df-7 12211

This theorem is referenced by:  7gbow  47960