Theorem gbpart7 46988

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 12348	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7414	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12367	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2755	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1533  (class class class)co 7404   + caddc 11112  2c2 12268  3c3 12269  4c4 12270  7c7 12273

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1789  ax-4 1803  ax-5 1905  ax-6 1963  ax-7 2003  ax-8 2100  ax-9 2108  ax-ext 2697  ax-1cn 11167  ax-addcl 11169  ax-addass 11174

This theorem depends on definitions:  df-bi 206  df-an 396  df-or 845  df-3an 1086  df-tru 1536  df-fal 1546  df-ex 1774  df-sb 2060  df-clab 2704  df-cleq 2718  df-clel 2804  df-rab 3427  df-v 3470  df-dif 3946  df-un 3948  df-in 3950  df-ss 3960  df-nul 4318  df-if 4524  df-sn 4624  df-pr 4626  df-op 4630  df-uni 4903  df-br 5142  df-iota 6488  df-fv 6544  df-ov 7407  df-2 12276  df-3 12277  df-4 12278  df-5 12279  df-6 12280  df-7 12281

This theorem is referenced by:  7gbow  46993