Theorem subsid1

Description: Identity law for subtraction. (Contributed by Scott Fenton, 3-Feb-2025)

	Ref	Expression
Assertion	subsid1	Could not format assertion : No typesetting found for |- ( A e. No -> ( A -s 0s ) = A ) with typecode |-

Proof

Step	Hyp	Ref	Expression
1		0sno	Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
2		subsval	Could not format ( ( A e. No /\ 0s e. No ) -> ( A -s 0s ) = ( A +s ( -us ` 0s ) ) ) : No typesetting found for |- ( ( A e. No /\ 0s e. No ) -> ( A -s 0s ) = ( A +s ( -us ` 0s ) ) ) with typecode |-
3	1 2	mpan2	Could not format ( A e. No -> ( A -s 0s ) = ( A +s ( -us ` 0s ) ) ) : No typesetting found for |- ( A e. No -> ( A -s 0s ) = ( A +s ( -us ` 0s ) ) ) with typecode |-
4		negs0s	Could not format ( -us ` 0s ) = 0s : No typesetting found for |- ( -us ` 0s ) = 0s with typecode |-
5	4	oveq2i	Could not format ( A +s ( -us ` 0s ) ) = ( A +s 0s ) : No typesetting found for |- ( A +s ( -us ` 0s ) ) = ( A +s 0s ) with typecode |-
6		addsrid	Could not format ( A e. No -> ( A +s 0s ) = A ) : No typesetting found for |- ( A e. No -> ( A +s 0s ) = A ) with typecode |-
7	5 6	eqtrid	Could not format ( A e. No -> ( A +s ( -us ` 0s ) ) = A ) : No typesetting found for |- ( A e. No -> ( A +s ( -us ` 0s ) ) = A ) with typecode |-
8	3 7	eqtrd	Could not format ( A e. No -> ( A -s 0s ) = A ) : No typesetting found for |- ( A e. No -> ( A -s 0s ) = A ) with typecode |-