Theorem gbpart7 47692

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 12399	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7441	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12418	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2764	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1537  (class class class)co 7431   + caddc 11156  2c2 12319  3c3 12320  4c4 12321  7c7 12324

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1792  ax-4 1806  ax-5 1908  ax-6 1965  ax-7 2005  ax-8 2108  ax-9 2116  ax-ext 2706  ax-1cn 11211  ax-addcl 11213  ax-addass 11218

This theorem depends on definitions:  df-bi 207  df-an 396  df-or 848  df-3an 1088  df-tru 1540  df-fal 1550  df-ex 1777  df-sb 2063  df-clab 2713  df-cleq 2727  df-clel 2814  df-rab 3434  df-v 3480  df-dif 3966  df-un 3968  df-ss 3980  df-nul 4340  df-if 4532  df-sn 4632  df-pr 4634  df-op 4638  df-uni 4913  df-br 5149  df-iota 6516  df-fv 6571  df-ov 7434  df-2 12327  df-3 12328  df-4 12329  df-5 12330  df-6 12331  df-7 12332

This theorem is referenced by:  7gbow  47697