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Theorem comraddd 7926
Description: Commute RHS addition, in deduction form. (Contributed by David A. Wheeler, 11-Oct-2018.)
Hypotheses
Ref Expression
comraddd.1  |-  ( ph  ->  B  e.  CC )
comraddd.2  |-  ( ph  ->  C  e.  CC )
comraddd.3  |-  ( ph  ->  A  =  ( B  +  C ) )
Assertion
Ref Expression
comraddd  |-  ( ph  ->  A  =  ( C  +  B ) )

Proof of Theorem comraddd
StepHypRef Expression
1 comraddd.3 . 2  |-  ( ph  ->  A  =  ( B  +  C ) )
2 comraddd.1 . . 3  |-  ( ph  ->  B  e.  CC )
3 comraddd.2 . . 3  |-  ( ph  ->  C  e.  CC )
42, 3addcomd 7920 . 2  |-  ( ph  ->  ( B  +  C
)  =  ( C  +  B ) )
51, 4eqtrd 2172 1  |-  ( ph  ->  A  =  ( C  +  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1331    e. wcel 1480  (class class class)co 5774   CCcc 7625    + caddc 7630
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 7727
This theorem depends on definitions:  df-bi 116  df-cleq 2132
This theorem is referenced by:  mvrladdd  8136  hashfz  10574  bdtrilem  11017  clim2ser2  11114  fsumparts  11246  arisum  11274  divalglemnn  11622  phiprmpw  11905  metrtri  12556  apdifflemr  13268
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