Theorem gbpart7 48455

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 12375	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7421	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12394	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2793	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1567  (class class class)co 7411   + caddc 11103  2c2 12295  3c3 12296  4c4 12297  7c7 12300

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1822  ax-4 1836  ax-5 1937  ax-6 1994  ax-7 2035  ax-8 2151  ax-9 2159  ax-ext 2741  ax-1cn 11158  ax-addcl 11160  ax-addass 11165

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1103  df-tru 1570  df-fal 1580  df-ex 1807  df-sb 2098  df-clab 2748  df-cleq 2761  df-clel 2844  df-rab 3424  df-v 3465  df-dif 3916  df-un 3918  df-ss 3930  df-nul 4295  df-if 4493  df-sn 4595  df-pr 4597  df-op 4601  df-uni 4877  df-br 5114  df-iota 6493  df-fv 6545  df-ov 7414  df-2 12303  df-3 12304  df-4 12305  df-5 12306  df-6 12307  df-7 12308

This theorem is referenced by:  7gbow  48460