Metamath Proof Explorer


Theorem subsf

Description: Function statement for surreal subtraction. (Contributed by Scott Fenton, 17-May-2025)

Ref Expression
Assertion subsf Could not format assertion : No typesetting found for |- -s : ( No X. No ) --> No with typecode |-

Proof

Step Hyp Ref Expression
1 negscl Could not format ( y e. No -> ( -us ` y ) e. No ) : No typesetting found for |- ( y e. No -> ( -us ` y ) e. No ) with typecode |-
2 addscl Could not format ( ( x e. No /\ ( -us ` y ) e. No ) -> ( x +s ( -us ` y ) ) e. No ) : No typesetting found for |- ( ( x e. No /\ ( -us ` y ) e. No ) -> ( x +s ( -us ` y ) ) e. No ) with typecode |-
3 1 2 sylan2 Could not format ( ( x e. No /\ y e. No ) -> ( x +s ( -us ` y ) ) e. No ) : No typesetting found for |- ( ( x e. No /\ y e. No ) -> ( x +s ( -us ` y ) ) e. No ) with typecode |-
4 3 rgen2 Could not format A. x e. No A. y e. No ( x +s ( -us ` y ) ) e. No : No typesetting found for |- A. x e. No A. y e. No ( x +s ( -us ` y ) ) e. No with typecode |-
5 df-subs Could not format -s = ( x e. No , y e. No |-> ( x +s ( -us ` y ) ) ) : No typesetting found for |- -s = ( x e. No , y e. No |-> ( x +s ( -us ` y ) ) ) with typecode |-
6 5 fmpo Could not format ( A. x e. No A. y e. No ( x +s ( -us ` y ) ) e. No <-> -s : ( No X. No ) --> No ) : No typesetting found for |- ( A. x e. No A. y e. No ( x +s ( -us ` y ) ) e. No <-> -s : ( No X. No ) --> No ) with typecode |-
7 4 6 mpbi Could not format -s : ( No X. No ) --> No : No typesetting found for |- -s : ( No X. No ) --> No with typecode |-