Theorem gbpart7 47877

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 12255	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7356	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12274	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2755	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1541  (class class class)co 7346   + caddc 11009  2c2 12180  3c3 12181  4c4 12182  7c7 12185

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 2113  ax-9 2121  ax-ext 2703  ax-1cn 11064  ax-addcl 11066  ax-addass 11071

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 2710  df-cleq 2723  df-clel 2806  df-rab 3396  df-v 3438  df-dif 3900  df-un 3902  df-ss 3914  df-nul 4281  df-if 4473  df-sn 4574  df-pr 4576  df-op 4580  df-uni 4857  df-br 5090  df-iota 6437  df-fv 6489  df-ov 7349  df-2 12188  df-3 12189  df-4 12190  df-5 12191  df-6 12192  df-7 12193

This theorem is referenced by:  7gbow  47882