Theorem gbpart9 48268

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 12320	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7367	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12328	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2763	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1547  (class class class)co 7357   + caddc 11033  3c3 12229  6c6 12232  9c9 12235

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1802  ax-4 1816  ax-5 1917  ax-6 1974  ax-7 2015  ax-8 2121  ax-9 2129  ax-ext 2711  ax-1cn 11088  ax-addcl 11090  ax-addass 11095

This theorem depends on definitions:  df-bi 208  df-an 397  df-or 854  df-3an 1094  df-tru 1550  df-fal 1560  df-ex 1787  df-sb 2074  df-clab 2718  df-cleq 2731  df-clel 2814  df-rab 3392  df-v 3433  df-dif 3886  df-un 3888  df-ss 3900  df-nul 4263  df-if 4456  df-sn 4557  df-pr 4559  df-op 4563  df-uni 4840  df-br 5074  df-iota 6442  df-fv 6494  df-ov 7360  df-2 12236  df-3 12237  df-4 12238  df-5 12239  df-6 12240  df-7 12241  df-8 12242  df-9 12243

This theorem is referenced by:  9gbo  48273