Theorem gbpart7 47754

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 12401	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7441	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12420	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2766	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1540  (class class class)co 7431   + caddc 11158  2c2 12321  3c3 12322  4c4 12323  7c7 12326

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1795  ax-4 1809  ax-5 1910  ax-6 1967  ax-7 2007  ax-8 2110  ax-9 2118  ax-ext 2708  ax-1cn 11213  ax-addcl 11215  ax-addass 11220

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 849  df-3an 1089  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2065  df-clab 2715  df-cleq 2729  df-clel 2816  df-rab 3437  df-v 3482  df-dif 3954  df-un 3956  df-ss 3968  df-nul 4334  df-if 4526  df-sn 4627  df-pr 4629  df-op 4633  df-uni 4908  df-br 5144  df-iota 6514  df-fv 6569  df-ov 7434  df-2 12329  df-3 12330  df-4 12331  df-5 12332  df-6 12333  df-7 12334

This theorem is referenced by:  7gbow  47759