Theorem gbpart7 48034

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 12277	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7368	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12296	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2760	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1541  (class class class)co 7358   + caddc 11031  2c2 12202  3c3 12203  4c4 12204  7c7 12207

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1796  ax-4 1810  ax-5 1911  ax-6 1968  ax-7 2009  ax-8 2115  ax-9 2123  ax-ext 2708  ax-1cn 11086  ax-addcl 11088  ax-addass 11093

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1544  df-fal 1554  df-ex 1781  df-sb 2068  df-clab 2715  df-cleq 2728  df-clel 2811  df-rab 3400  df-v 3442  df-dif 3904  df-un 3906  df-ss 3918  df-nul 4286  df-if 4480  df-sn 4581  df-pr 4583  df-op 4587  df-uni 4864  df-br 5099  df-iota 6448  df-fv 6500  df-ov 7361  df-2 12210  df-3 12211  df-4 12212  df-5 12213  df-6 12214  df-7 12215

This theorem is referenced by:  7gbow  48039