Theorem gbpart9 47694

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 12416	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7441	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12424	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2764	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1537  (class class class)co 7431   + caddc 11156  3c3 12320  6c6 12323  9c9 12326

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-1cn 11211  ax-addcl 11213  ax-addass 11218

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-2 12327  df-3 12328  df-4 12329  df-5 12330  df-6 12331  df-7 12332  df-8 12333  df-9 12334

This theorem is referenced by:  9gbo  47699