Theorem addscan1

Description: Cancellation law for surreal addition. (Contributed by Scott Fenton, 21-Jan-2025)

	Ref	Expression
Assertion	addscan1	Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( C +s A ) = ( C +s B ) <-> A = B ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		addscom	Could not format ( ( A e. No /\ C e. No ) -> ( A +s C ) = ( C +s A ) ) : No typesetting found for |- ( ( A e. No /\ C e. No ) -> ( A +s C ) = ( C +s A ) ) with typecode |-
2	1	3adant2	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( A +s C ) = ( C +s A ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A +s C ) = ( C +s A ) ) with typecode |-
3		addscom	Could not format ( ( B e. No /\ C e. No ) -> ( B +s C ) = ( C +s B ) ) : No typesetting found for |- ( ( B e. No /\ C e. No ) -> ( B +s C ) = ( C +s B ) ) with typecode |-
4	3	3adant1	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( B +s C ) = ( C +s B ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( B +s C ) = ( C +s B ) ) with typecode |-
5	2 4	eqeq12d	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A +s C ) = ( B +s C ) <-> ( C +s A ) = ( C +s B ) ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A +s C ) = ( B +s C ) <-> ( C +s A ) = ( C +s B ) ) ) with typecode |-
6		addscan2	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A +s C ) = ( B +s C ) <-> A = B ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A +s C ) = ( B +s C ) <-> A = B ) ) with typecode |-
7	5 6	bitr3d	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( C +s A ) = ( C +s B ) <-> A = B ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( C +s A ) = ( C +s B ) <-> A = B ) ) with typecode |-