Theorem pncan3s

Description: Subtraction and addition of equals. (Contributed by Scott Fenton, 4-Feb-2025)

	Ref	Expression
Assertion	pncan3s	Could not format assertion : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( A +s ( B -s A ) ) = B ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		eqid	Could not format ( B -s A ) = ( B -s A ) : No typesetting found for |- ( B -s A ) = ( B -s A ) with typecode |-
2		simpr	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to B\in \mathrm{No}$$
3		simpl	$$⊢\left(A\in \mathrm{No}\wedge B\in \mathrm{No}\right)\to A\in \mathrm{No}$$
4	2 3	subscld	Could not format ( ( A e. No /\ B e. No ) -> ( B -s A ) e. No ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( B -s A ) e. No ) with typecode |-
5	2 3 4	subaddsd	Could not format ( ( A e. No /\ B e. No ) -> ( ( B -s A ) = ( B -s A ) <-> ( A +s ( B -s A ) ) = B ) ) : No typesetting found for |- ( ( A e. No /\ B e. No ) -> ( ( B -s A ) = ( B -s A ) <-> ( A +s ( B -s A ) ) = B ) ) with typecode |-
6	1 5	mpbii	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 |-