Theorem gbpart7 47772

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 12323	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7400	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12342	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2754	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1540  (class class class)co 7390   + caddc 11078  2c2 12248  3c3 12249  4c4 12250  7c7 12253

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 2008  ax-8 2111  ax-9 2119  ax-ext 2702  ax-1cn 11133  ax-addcl 11135  ax-addass 11140

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2709  df-cleq 2722  df-clel 2804  df-rab 3409  df-v 3452  df-dif 3920  df-un 3922  df-ss 3934  df-nul 4300  df-if 4492  df-sn 4593  df-pr 4595  df-op 4599  df-uni 4875  df-br 5111  df-iota 6467  df-fv 6522  df-ov 7393  df-2 12256  df-3 12257  df-4 12258  df-5 12259  df-6 12260  df-7 12261

This theorem is referenced by:  7gbow  47777