Metamath Proof Explorer


Theorem muls02

Description: Surreal multiplication by zero. (Contributed by Scott Fenton, 4-Feb-2025)

Ref Expression
Assertion muls02 Could not format assertion : No typesetting found for |- ( A e. No -> ( 0s x.s A ) = 0s ) with typecode |-

Proof

Step Hyp Ref Expression
1 0sno Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
2 mulscom Could not format ( ( 0s e. No /\ A e. No ) -> ( 0s x.s A ) = ( A x.s 0s ) ) : No typesetting found for |- ( ( 0s e. No /\ A e. No ) -> ( 0s x.s A ) = ( A x.s 0s ) ) with typecode |-
3 1 2 mpan Could not format ( A e. No -> ( 0s x.s A ) = ( A x.s 0s ) ) : No typesetting found for |- ( A e. No -> ( 0s x.s A ) = ( A x.s 0s ) ) with typecode |-
4 muls01 Could not format ( A e. No -> ( A x.s 0s ) = 0s ) : No typesetting found for |- ( A e. No -> ( A x.s 0s ) = 0s ) with typecode |-
5 3 4 eqtrd Could not format ( A e. No -> ( 0s x.s A ) = 0s ) : No typesetting found for |- ( A e. No -> ( 0s x.s A ) = 0s ) with typecode |-