Theorem gbpart7 48390

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 12353	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7407	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12372	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2787	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1561  (class class class)co 7397   + caddc 11077  2c2 12273  3c3 12274  4c4 12275  7c7 12278

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1816  ax-4 1830  ax-5 1931  ax-6 1988  ax-7 2029  ax-8 2145  ax-9 2153  ax-ext 2735  ax-1cn 11132  ax-addcl 11134  ax-addass 11139

This theorem depends on definitions:  df-bi 209  df-an 400  df-or 859  df-3an 1101  df-tru 1564  df-fal 1574  df-ex 1801  df-sb 2092  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3416  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4482  df-sn 4584  df-pr 4586  df-op 4590  df-uni 4867  df-br 5102  df-iota 6478  df-fv 6530  df-ov 7400  df-2 12281  df-3 12282  df-4 12283  df-5 12284  df-6 12285  df-7 12286

This theorem is referenced by:  7gbow  48395