Theorem gbpart9 47111

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 12400	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7434	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12408	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2756	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1533  (class class class)co 7424   + caddc 11147  3c3 12304  6c6 12307  9c9 12310

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2698  ax-1cn 11202  ax-addcl 11204  ax-addass 11209

This theorem depends on definitions:  df-bi 206  df-an 395  df-or 846  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2705  df-cleq 2719  df-clel 2805  df-rab 3429  df-v 3473  df-dif 3950  df-un 3952  df-in 3954  df-ss 3964  df-nul 4325  df-if 4531  df-sn 4631  df-pr 4633  df-op 4637  df-uni 4911  df-br 5151  df-iota 6503  df-fv 6559  df-ov 7427  df-2 12311  df-3 12312  df-4 12313  df-5 12314  df-6 12315  df-7 12316  df-8 12317  df-9 12318

This theorem is referenced by:  9gbo  47116