Metamath Proof Explorer


Theorem sltadd1im

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

Ref Expression
Assertion sltadd1im Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( A ( A +s C )

Proof

Step Hyp Ref Expression
1 addsprop Could not format ( ( C e. No /\ A e. No /\ B e. No ) -> ( ( C +s A ) e. No /\ ( A ( A +s C ) ( ( C +s A ) e. No /\ ( A ( A +s C )
2 1 3coml Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( C +s A ) e. No /\ ( A ( A +s C ) ( ( C +s A ) e. No /\ ( A ( A +s C )
3 2 simprd Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( A ( A +s C ) ( A ( A +s C )