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Theorem comraddd 7639
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 7633 . 2  |-  ( ph  ->  ( B  +  C
)  =  ( C  +  B ) )
51, 4eqtrd 2120 1  |-  ( ph  ->  A  =  ( C  +  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1289    e. wcel 1438  (class class class)co 5652   CCcc 7348    + caddc 7353
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 104  ax-ia2 105  ax-ia3 106  ax-5 1381  ax-gen 1383  ax-4 1445  ax-17 1464  ax-ext 2070  ax-addcom 7445
This theorem depends on definitions:  df-bi 115  df-cleq 2081
This theorem is referenced by:  hashfz  10229  clim2ser2  10726  fsumparts  10864  arisum  10892  divalglemnn  11196  phiprmpw  11476
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