Theorem subaddsd

Description: Relationship between addition and subtraction for surreals. (Contributed by Scott Fenton, 5-Feb-2025)

	Ref	Expression
Hypotheses	subaddsd.1	$$⊢\phi \to A\in \mathrm{No}$$
	subaddsd.2	$$⊢\phi \to B\in \mathrm{No}$$
	subaddsd.3	$$⊢\phi \to C\in \mathrm{No}$$
Assertion	subaddsd	Could not format assertion : No typesetting found for |- ( ph -> ( ( A -s B ) = C <-> ( B +s C ) = A ) ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		subaddsd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		subaddsd.2	$$⊢\phi \to B\in \mathrm{No}$$
3		subaddsd.3	$$⊢\phi \to C\in \mathrm{No}$$
4		subadds	Could not format ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A -s B ) = C <-> ( B +s C ) = A ) ) : No typesetting found for |- ( ( A e. No /\ B e. No /\ C e. No ) -> ( ( A -s B ) = C <-> ( B +s C ) = A ) ) with typecode |-
5	1 2 3 4	syl3anc	Could not format ( ph -> ( ( A -s B ) = C <-> ( B +s C ) = A ) ) : No typesetting found for |- ( ph -> ( ( A -s B ) = C <-> ( B +s C ) = A ) ) with typecode |-