Theorem gbpart9 47643

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 12445	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7458	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12453	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2769	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1537  (class class class)co 7448   + caddc 11187  3c3 12349  6c6 12352  9c9 12355

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1793  ax-4 1807  ax-5 1909  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2711  ax-1cn 11242  ax-addcl 11244  ax-addass 11249

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 847  df-3an 1089  df-tru 1540  df-fal 1550  df-ex 1778  df-sb 2065  df-clab 2718  df-cleq 2732  df-clel 2819  df-rab 3444  df-v 3490  df-dif 3979  df-un 3981  df-ss 3993  df-nul 4353  df-if 4549  df-sn 4649  df-pr 4651  df-op 4655  df-uni 4932  df-br 5167  df-iota 6525  df-fv 6581  df-ov 7451  df-2 12356  df-3 12357  df-4 12358  df-5 12359  df-6 12360  df-7 12361  df-8 12362  df-9 12363

This theorem is referenced by:  9gbo  47648