Theorem gbpart7 44285

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 11760	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7145	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 11779	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2822	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1538  (class class class)co 7135   + caddc 10529  2c2 11680  3c3 11681  4c4 11682  7c7 11685

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 1911  ax-6 1970  ax-7 2015  ax-8 2113  ax-9 2121  ax-ext 2770  ax-1cn 10584  ax-addcl 10586  ax-addass 10591

This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2070  df-clab 2777  df-cleq 2791  df-clel 2870  df-v 3443  df-un 3886  df-in 3888  df-ss 3898  df-sn 4526  df-pr 4528  df-op 4532  df-uni 4801  df-br 5031  df-iota 6283  df-fv 6332  df-ov 7138  df-2 11688  df-3 11689  df-4 11690  df-5 11691  df-6 11692  df-7 11693

This theorem is referenced by:  7gbow  44290