Theorem gbpart9 48554

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 12387	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7420	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12395	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2787	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1570  (class class class)co 7410   + caddc 11098  3c3 12291  6c6 12294  9c9 12297

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-1cn 11153  ax-addcl 11155  ax-addass 11160

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-iota 6492  df-fv 6544  df-ov 7413  df-2 12298  df-3 12299  df-4 12300  df-5 12301  df-6 12302  df-7 12303  df-8 12304  df-9 12305

This theorem is referenced by:  9gbo  48559