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Theorem addcomi 7319
Description: Addition commutes. Based on ideas by Eric Schmidt. (Contributed by Scott Fenton, 3-Jan-2013.)
Hypotheses
Ref Expression
mul.1 𝐴 ∈ ℂ
mul.2 𝐵 ∈ ℂ
Assertion
Ref Expression
addcomi (𝐴 + 𝐵) = (𝐵 + 𝐴)

Proof of Theorem addcomi
StepHypRef Expression
1 mul.1 . 2 𝐴 ∈ ℂ
2 mul.2 . 2 𝐵 ∈ ℂ
3 addcom 7312 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) = (𝐵 + 𝐴))
41, 2, 3mp2an 417 1 (𝐴 + 𝐵) = (𝐵 + 𝐴)
Colors of variables: wff set class
Syntax hints:   = wceq 1285  wcel 1434  (class class class)co 5543  cc 7041   + caddc 7046
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia3 106  ax-addcom 7138
This theorem is referenced by:  addcomli  7320  add42i  7341  mvlladdi  7393  3m1e2  8225  fztpval  9176  fzo0to42pr  9306
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