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Theorem comraddd 8127
Description: Commute RHS addition, in deduction form. (Contributed by David A. Wheeler, 11-Oct-2018.)
Hypotheses
Ref Expression
comraddd.1 (𝜑𝐵 ∈ ℂ)
comraddd.2 (𝜑𝐶 ∈ ℂ)
comraddd.3 (𝜑𝐴 = (𝐵 + 𝐶))
Assertion
Ref Expression
comraddd (𝜑𝐴 = (𝐶 + 𝐵))

Proof of Theorem comraddd
StepHypRef Expression
1 comraddd.3 . 2 (𝜑𝐴 = (𝐵 + 𝐶))
2 comraddd.1 . . 3 (𝜑𝐵 ∈ ℂ)
3 comraddd.2 . . 3 (𝜑𝐶 ∈ ℂ)
42, 3addcomd 8121 . 2 (𝜑 → (𝐵 + 𝐶) = (𝐶 + 𝐵))
51, 4eqtrd 2220 1 (𝜑𝐴 = (𝐶 + 𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1363  wcel 2158  (class class class)co 5888  cc 7822   + caddc 7827
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106  ax-ia2 107  ax-ia3 108  ax-5 1457  ax-gen 1459  ax-4 1520  ax-17 1536  ax-ext 2169  ax-addcom 7924
This theorem depends on definitions:  df-bi 117  df-cleq 2180
This theorem is referenced by:  mvrladdd  8337  hashfz  10814  bdtrilem  11260  clim2ser2  11359  fsumparts  11491  arisum  11519  divalglemnn  11936  phiprmpw  12235  mulgdir  13044  metrtri  14117  apdifflemr  15036
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