Metamath Proof Explorer


Theorem sn-subf

Description: subf without ax-mulcom . (Contributed by SN, 5-May-2024)

Ref Expression
Assertion sn-subf :×

Proof

Step Hyp Ref Expression
1 subval xyxy=ιz|y+z=x
2 sn-subcl xyxy
3 1 2 eqeltrrd xyιz|y+z=x
4 3 rgen2 xyιz|y+z=x
5 df-sub =x,yιz|y+z=x
6 5 fmpo xyιz|y+z=x:×
7 4 6 mpbi :×