Theorem recsexd

Description: A non-zero surreal has a reciprocal. (Contributed by Scott Fenton, 16-Mar-2025)

	Ref	Expression
Hypotheses	recsexd.1	|- ( ph -> A e. No )
	recsexd.2	|- ( ph -> A =/= 0s )
Assertion	recsexd	|- ( ph -> E. x e. No ( A x.s x ) = 1s )

Proof

Step	Hyp	Ref	Expression
1		recsexd.1	|- ( ph -> A e. No )
2		recsexd.2	|- ( ph -> A =/= 0s )
3		recsex	|- ( ( A e. No /\ A =/= 0s ) -> E. x e. No ( A x.s x ) = 1s )
4	1 2 3	syl2anc	|- ( ph -> E. x e. No ( A x.s x ) = 1s )