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Theorem comraddd 7933
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 7927 . 2 (𝜑 → (𝐵 + 𝐶) = (𝐶 + 𝐵))
51, 4eqtrd 2172 1 (𝜑𝐴 = (𝐶 + 𝐵))
Colors of variables: wff set class
Syntax hints:  wi 4   = wceq 1331  wcel 1480  (class class class)co 5774  cc 7632   + caddc 7637
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 105  ax-ia2 106  ax-ia3 107  ax-5 1423  ax-gen 1425  ax-4 1487  ax-17 1506  ax-ext 2121  ax-addcom 7734
This theorem depends on definitions:  df-bi 116  df-cleq 2132
This theorem is referenced by:  mvrladdd  8143  hashfz  10581  bdtrilem  11024  clim2ser2  11121  fsumparts  11253  arisum  11281  divalglemnn  11628  phiprmpw  11911  metrtri  12562  apdifflemr  13349
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