Theorem sltadd1im

Description: Surreal less-than is preserved under addition. (Contributed by Scott Fenton, 21-Jan-2025)

	Ref	Expression
Assertion	sltadd1im	|- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A ( A +s C )

Proof

Step	Hyp	Ref	Expression
1		addsprop	|- ( ( C e. No /\ A e. No /\ B e. No ) -> ( ( C +s A ) e. No /\ ( A ( A +s C )
2	1	3coml	|- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( C +s A ) e. No /\ ( A ( A +s C )
3	2	simprd	|- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A ( A +s C )