Theorem gbpart7 48552

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 12370	. . 3 ⊢ (2 + 2) = 4
2	1	oveq1i 7420	. 2 ⊢ ((2 + 2) + 3) = (4 + 3)
3		4p3e7 12389	. 2 ⊢ (4 + 3) = 7
4	2, 3	eqtr2i 2787	1 ⊢ 7 = ((2 + 2) + 3)

Syntax hints:   = wceq 1570  (class class class)co 7410   + caddc 11098  2c2 12290  3c3 12291  4c4 12292  7c7 12295

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1825  ax-4 1839  ax-5 1940  ax-6 1997  ax-7 2038  ax-8 2145  ax-9 2153  ax-ext 2735  ax-1cn 11153  ax-addcl 11155  ax-addass 11160

This theorem depends on definitions:  df-bi 210  df-an 401  df-or 861  df-3an 1105  df-tru 1573  df-fal 1583  df-ex 1810  df-sb 2097  df-clab 2742  df-cleq 2755  df-clel 2838  df-rab 3417  df-v 3457  df-dif 3908  df-un 3910  df-ss 3922  df-nul 4287  df-if 4488  df-sn 4590  df-pr 4592  df-op 4596  df-uni 4873  df-br 5110  df-iota 6492  df-fv 6544  df-ov 7413  df-2 12298  df-3 12299  df-4 12300  df-5 12301  df-6 12302  df-7 12303

This theorem is referenced by:  7gbow  48557