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Theorem comraddd 7384
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 7378 . 2  |-  ( ph  ->  ( B  +  C
)  =  ( C  +  B ) )
51, 4eqtrd 2115 1  |-  ( ph  ->  A  =  ( C  +  B ) )
Colors of variables: wff set class
Syntax hints:    -> wi 4    = wceq 1285    e. wcel 1434  (class class class)co 5563   CCcc 7093    + caddc 7098
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 1377  ax-gen 1379  ax-4 1441  ax-17 1460  ax-ext 2065  ax-addcom 7190
This theorem depends on definitions:  df-bi 115  df-cleq 2076
This theorem is referenced by:  hashfz  9897  divalglemnn  10525  phiprmpw  10805
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