Theorem gbpart7 47755

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 12258	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7359	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12277	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2753	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1540  (class class class)co 7349   + caddc 11012  2c2 12183  3c3 12184  4c4 12185  7c7 12188

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 2701  ax-1cn 11067  ax-addcl 11069  ax-addass 11074

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 2708  df-cleq 2721  df-clel 2803  df-rab 3395  df-v 3438  df-dif 3906  df-un 3908  df-ss 3920  df-nul 4285  df-if 4477  df-sn 4578  df-pr 4580  df-op 4584  df-uni 4859  df-br 5093  df-iota 6438  df-fv 6490  df-ov 7352  df-2 12191  df-3 12192  df-4 12193  df-5 12194  df-6 12195  df-7 12196

This theorem is referenced by:  7gbow  47760