Theorem expscl

Description: Closure law for surreal exponentiation. (Contributed by Scott Fenton, 7-Aug-2025)

	Ref	Expression
Assertion	expscl	Could not format assertion : No typesetting found for |- ( ( A e. No /\ N e. NN0_s ) -> ( A ^su N ) e. No ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		ssid	$$⊢\mathrm{No}\subseteq \mathrm{No}$$
2		mulscl	$$⊢\left(x\in \mathrm{No}\wedge y\in \mathrm{No}\right)\to x{\cdot }_{s}y\in \mathrm{No}$$
3		1sno	$$⊢1_s\in \mathrm{No}$$
4	1 2 3	expscllem	Could not format ( ( A e. No /\ N e. NN0_s ) -> ( A ^su N ) e. No ) : No typesetting found for |- ( ( A e. No /\ N e. NN0_s ) -> ( A ^su N ) e. No ) with typecode |-