Metamath Proof Explorer


Theorem mvrraddd

Description: Move the right term in a sum on the RHS to the LHS, deduction form. (Contributed by David A. Wheeler, 11-Oct-2018)

Ref Expression
Hypotheses mvrraddd.1
|- ( ph -> B e. CC )
mvrraddd.2
|- ( ph -> C e. CC )
mvrraddd.3
|- ( ph -> A = ( B + C ) )
Assertion mvrraddd
|- ( ph -> ( A - C ) = B )

Proof

Step Hyp Ref Expression
1 mvrraddd.1
 |-  ( ph -> B e. CC )
2 mvrraddd.2
 |-  ( ph -> C e. CC )
3 mvrraddd.3
 |-  ( ph -> A = ( B + C ) )
4 3 oveq1d
 |-  ( ph -> ( A - C ) = ( ( B + C ) - C ) )
5 1 2 pncand
 |-  ( ph -> ( ( B + C ) - C ) = B )
6 4 5 eqtrd
 |-  ( ph -> ( A - C ) = B )