Theorem gbpart9 47770

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 12333	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7397	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12341	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2753	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1540  (class class class)co 7387   + caddc 11071  3c3 12242  6c6 12245  9c9 12248

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-1cn 11126  ax-addcl 11128  ax-addass 11133

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rab 3406  df-v 3449  df-dif 3917  df-un 3919  df-ss 3931  df-nul 4297  df-if 4489  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4872  df-br 5108  df-iota 6464  df-fv 6519  df-ov 7390  df-2 12249  df-3 12250  df-4 12251  df-5 12252  df-6 12253  df-7 12254  df-8 12255  df-9 12256

This theorem is referenced by:  9gbo  47775