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Theorem addcomi 7918
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 7911 . 2 ((𝐴 ∈ ℂ ∧ 𝐵 ∈ ℂ) → (𝐴 + 𝐵) = (𝐵 + 𝐴))
41, 2, 3mp2an 422 1 (𝐴 + 𝐵) = (𝐵 + 𝐴)
Colors of variables: wff set class
Syntax hints:   = wceq 1331  wcel 1480  (class class class)co 5774  cc 7630   + caddc 7635
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia3 107  ax-addcom 7732
This theorem is referenced by:  addcomli  7919  add42i  7940  mvlladdi  7992  3m1e2  8852  fztpval  9875  fzo0to42pr  10009  ef01bndlem  11474  tangtx  12941
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