Theorem gbpart9 44287

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 11777	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7145	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 11785	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2822	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1538  (class class class)co 7135   + caddc 10529  3c3 11681  6c6 11684  9c9 11687

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-1cn 10584  ax-addcl 10586  ax-addass 10591

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-iota 6283  df-fv 6332  df-ov 7138  df-2 11688  df-3 11689  df-4 11690  df-5 11691  df-6 11692  df-7 11693  df-8 11694  df-9 11695

This theorem is referenced by:  9gbo  44292