Metamath Proof Explorer


Theorem comraddd

Description: Commute RHS addition, in deduction form. (Contributed by David A. Wheeler, 11-Oct-2018)

Ref Expression
Hypotheses comraddd.1 φB
comraddd.2 φC
comraddd.3 φA=B+C
Assertion comraddd φA=C+B

Proof

Step Hyp Ref Expression
1 comraddd.1 φB
2 comraddd.2 φC
3 comraddd.3 φA=B+C
4 1 2 addcomd φB+C=C+B
5 3 4 eqtrd φA=C+B