Theorem gbpart9 48036

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 12294	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7368	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12302	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2760	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1541  (class class class)co 7358   + caddc 11031  3c3 12203  6c6 12206  9c9 12209

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708  ax-1cn 11086  ax-addcl 11088  ax-addass 11093

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-uni 4864  df-br 5099  df-iota 6448  df-fv 6500  df-ov 7361  df-2 12210  df-3 12211  df-4 12212  df-5 12213  df-6 12214  df-7 12215  df-8 12216  df-9 12217

This theorem is referenced by:  9gbo  48041