Theorem gbpart9 45173

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 12108	. . 3 ⊢ (3 + 3) = 6
2	1	oveq1i 7278	. 2 ⊢ ((3 + 3) + 3) = (6 + 3)
3		6p3e9 12116	. 2 ⊢ (6 + 3) = 9
4	2, 3	eqtr2i 2768	1 ⊢ 9 = ((3 + 3) + 3)

Syntax hints:   = wceq 1541  (class class class)co 7268   + caddc 10858  3c3 12012  6c6 12015  9c9 12018

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1801  ax-4 1815  ax-5 1916  ax-6 1974  ax-7 2014  ax-8 2111  ax-9 2119  ax-ext 2710  ax-1cn 10913  ax-addcl 10915  ax-addass 10920

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 844  df-3an 1087  df-tru 1544  df-fal 1554  df-ex 1786  df-sb 2071  df-clab 2717  df-cleq 2731  df-clel 2817  df-rab 3074  df-v 3432  df-dif 3894  df-un 3896  df-in 3898  df-ss 3908  df-nul 4262  df-if 4465  df-sn 4567  df-pr 4569  df-op 4573  df-uni 4845  df-br 5079  df-iota 6388  df-fv 6438  df-ov 7271  df-2 12019  df-3 12020  df-4 12021  df-5 12022  df-6 12023  df-7 12024  df-8 12025  df-9 12026

This theorem is referenced by:  9gbo  45178