Theorem gbpart9 46427

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 12363	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7418	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12371	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2761	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1541  (class class class)co 7408   + caddc 11112  3c3 12267  6c6 12270  9c9 12273

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 1913  ax-6 1971  ax-7 2011  ax-8 2108  ax-9 2116  ax-ext 2703  ax-1cn 11167  ax-addcl 11169  ax-addass 11174

This theorem depends on definitions:  df-bi 206  df-an 397  df-or 846  df-3an 1089  df-tru 1544  df-fal 1554  df-ex 1782  df-sb 2068  df-clab 2710  df-cleq 2724  df-clel 2810  df-rab 3433  df-v 3476  df-dif 3951  df-un 3953  df-in 3955  df-ss 3965  df-nul 4323  df-if 4529  df-sn 4629  df-pr 4631  df-op 4635  df-uni 4909  df-br 5149  df-iota 6495  df-fv 6551  df-ov 7411  df-2 12274  df-3 12275  df-4 12276  df-5 12277  df-6 12278  df-7 12279  df-8 12280  df-9 12281

This theorem is referenced by:  9gbo  46432