Theorem gbpart7 47748

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 12380	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7420	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12399	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2760	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1540  (class class class)co 7410   + caddc 11137  2c2 12300  3c3 12301  4c4 12302  7c7 12305

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 2708  ax-1cn 11192  ax-addcl 11194  ax-addass 11199

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 2715  df-cleq 2728  df-clel 2810  df-rab 3421  df-v 3466  df-dif 3934  df-un 3936  df-ss 3948  df-nul 4314  df-if 4506  df-sn 4607  df-pr 4609  df-op 4613  df-uni 4889  df-br 5125  df-iota 6489  df-fv 6544  df-ov 7413  df-2 12308  df-3 12309  df-4 12310  df-5 12311  df-6 12312  df-7 12313

This theorem is referenced by:  7gbow  47753