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Theorem gbpart7 44211
 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
StepHypRef Expression
1 2p2e4 11769 . . 3 (2 + 2) = 4
21oveq1i 7159 . 2 ((2 + 2) + 3) = (4 + 3)
3 4p3e7 11788 . 2 (4 + 3) = 7
42, 3eqtr2i 2848 1 7 = ((2 + 2) + 3)
 Colors of variables: wff setvar class Syntax hints:   = wceq 1538  (class class class)co 7149   + caddc 10538  2c2 11689  3c3 11690  4c4 11691  7c7 11694 This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1797  ax-4 1811  ax-5 1912  ax-6 1971  ax-7 2016  ax-8 2117  ax-9 2125  ax-ext 2796  ax-1cn 10593  ax-addcl 10595  ax-addass 10600 This theorem depends on definitions:  df-bi 210  df-an 400  df-or 845  df-3an 1086  df-ex 1782  df-sb 2071  df-clab 2803  df-cleq 2817  df-clel 2896  df-v 3482  df-un 3924  df-in 3926  df-ss 3936  df-sn 4551  df-pr 4553  df-op 4557  df-uni 4825  df-br 5053  df-iota 6302  df-fv 6351  df-ov 7152  df-2 11697  df-3 11698  df-4 11699  df-5 11700  df-6 11701  df-7 11702 This theorem is referenced by:  7gbow  44216
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