Theorem gbpart9 48611

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 12411	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7429	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12419	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2789	1 ⊢ 9 = ((3 + 3) + 3)

This proof depends on syntax axioms:   = wceq 1570  (class class class)co 7419   + caddc 11122  3c3 12315  6c6 12318  9c9 12321

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1828  ax-4 1842  ax-5 1943  ax-6 2000  ax-7 2041  ax-8 2148  ax-9 2156  ax-ext 2737  ax-1cn 11177  ax-addcl 11179  ax-addass 11184

This proof depends on definitions:  df-bi 210  df-an 402  df-or 862  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1813  df-sb 2100  df-clab 2744  df-cleq 2757  df-clel 2840  df-rab 3419  df-v 3459  df-dif 3909  df-un 3911  df-ss 3923  df-nul 4287  df-if 4490  df-sn 4592  df-pr 4594  df-op 4598  df-uni 4875  df-br 5112  df-iota 6496  df-fv 6548  df-ov 7422  df-2 12322  df-3 12323  df-4 12324  df-5 12325  df-6 12326  df-7 12327  df-8 12328  df-9 12329

This theorem is used by:  9gbo  48616