Theorem nncansd

Description: Cancellation law for surreal subtraction. (Contributed by Scott Fenton, 16-Apr-2025)

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

Proof

Step	Hyp	Ref	Expression
1		nncansd.1	$$⊢\phi \to A\in \mathrm{No}$$
2		nncansd.2	$$⊢\phi \to B\in \mathrm{No}$$
3	1 1 2	subsubs2d	Could not format ( ph -> ( A -s ( A -s B ) ) = ( A +s ( B -s A ) ) ) : No typesetting found for |- ( ph -> ( A -s ( A -s B ) ) = ( A +s ( B -s A ) ) ) with typecode |-
4		pncan3s	Could not format ( ( A e. No /\ B e. No ) -> ( A +s ( B -s A ) ) = B ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A +s ( B -s A ) ) = B ) with typecode |-
5	1 2 4	syl2anc	Could not format ( ph -> ( A +s ( B -s A ) ) = B ) : No typesetting found for |- ( ph -> ( A +s ( B -s A ) ) = B ) with typecode |-
6	3 5	eqtrd	Could not format ( ph -> ( A -s ( A -s B ) ) = B ) : No typesetting found for |- ( ph -> ( A -s ( A -s B ) ) = B ) with typecode |-