Theorem gbpart7 47768

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 12316	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7397	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12335	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2753	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1540  (class class class)co 7387   + caddc 11071  2c2 12241  3c3 12242  4c4 12243  7c7 12246

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 2008  ax-8 2111  ax-9 2119  ax-ext 2701  ax-1cn 11126  ax-addcl 11128  ax-addass 11133

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1543  df-fal 1553  df-ex 1780  df-sb 2066  df-clab 2708  df-cleq 2721  df-clel 2803  df-rab 3406  df-v 3449  df-dif 3917  df-un 3919  df-ss 3931  df-nul 4297  df-if 4489  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4872  df-br 5108  df-iota 6464  df-fv 6519  df-ov 7390  df-2 12249  df-3 12250  df-4 12251  df-5 12252  df-6 12253  df-7 12254

This theorem is referenced by:  7gbow  47773