Metamath Proof Explorer


Theorem rsubrotld

Description: Rotate the variables left in an equation with subtraction on the right, converting it into an addition.

EDITORIAL: The label for this theorem is questionable. Do not move until it would have 7 uses: current additional uses: (none). (Contributed by SN, 4-Jul-2025)

Ref Expression
Hypotheses rsubrotld.b φ B
rsubrotld.c φ C
rsubrotld.1 φ A = B C
Assertion rsubrotld φ B = C + A

Proof

Step Hyp Ref Expression
1 rsubrotld.b φ B
2 rsubrotld.c φ C
3 rsubrotld.1 φ A = B C
4 3 eqcomd φ B C = A
5 1 2 4 lsubrotld φ C + A = B
6 5 eqcomd φ B = C + A