Metamath Proof Explorer


Theorem subsval

Description: The value of surreal subtraction. (Contributed by Scott Fenton, 3-Feb-2025)

Ref Expression
Assertion subsval A No B No A - s B = A + s + s B

Proof

Step Hyp Ref Expression
1 oveq1 x = A x + s + s y = A + s + s y
2 fveq2 y = B + s y = + s B
3 2 oveq2d y = B A + s + s y = A + s + s B
4 df-subs - s = x No , y No x + s + s y
5 ovex A + s + s B V
6 1 3 4 5 ovmpo A No B No A - s B = A + s + s B