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

Step	Hyp	Ref	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 )
4	2, 3	addcomd 7633	. 2 |- ( ph -> ( B + C ) = ( C + B ) )
5	1, 4	eqtrd 2120	1 |- ( ph -> A = ( C + B ) )

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