Theorem gbpart9 48392

Description: The (strong) Goldbach partition of 9. (Contributed by AV, 26-Jul-2020.)

Assertion

Ref	Expression
gbpart9	⊢ 9 = ((3 + 3) + 3)

Proof of Theorem gbpart9

Step	Hyp	Ref	Expression
1		3p3e6 12370	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7407	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12378	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2787	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1561  (class class class)co 7397   + caddc 11077  3c3 12274  6c6 12277  9c9 12280

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  df-8 12287  df-9 12288

This theorem is referenced by:  9gbo  48397