Theorem gbpart7 48258

Description: The (weak) Goldbach partition of 7. (Contributed by AV, 20-Jul-2020.)

Assertion

Ref	Expression
gbpart7	⊢ 7 = ((2 + 2) + 3)

Proof of Theorem gbpart7

Step	Hyp	Ref	Expression
1		2p2e4 12305	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7371	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12324	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2761	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1542  (class class class)co 7361   + caddc 11035  2c2 12230  3c3 12231  4c4 12232  7c7 12235

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1969  ax-7 2010  ax-8 2116  ax-9 2124  ax-ext 2709  ax-1cn 11090  ax-addcl 11092  ax-addass 11097

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1545  df-fal 1555  df-ex 1782  df-sb 2069  df-clab 2716  df-cleq 2729  df-clel 2812  df-rab 3391  df-v 3432  df-dif 3893  df-un 3895  df-ss 3907  df-nul 4275  df-if 4468  df-sn 4569  df-pr 4571  df-op 4575  df-uni 4852  df-br 5087  df-iota 6449  df-fv 6501  df-ov 7364  df-2 12238  df-3 12239  df-4 12240  df-5 12241  df-6 12242  df-7 12243

This theorem is referenced by:  7gbow  48263