Theorem sltaddpos1d

Description: Addition of a positive number increases the sum. (Contributed by Scott Fenton, 15-Apr-2025)

	Ref	Expression
Hypotheses	sltaddpos.1	|- ( ph -> A e. No )
	sltaddpos.2	|- ( ph -> B e. No )
Assertion	sltaddpos1d	|- ( ph -> ( 0s B

Proof

Step	Hyp	Ref	Expression
1		sltaddpos.1	|- ( ph -> A e. No )
2		sltaddpos.2	|- ( ph -> B e. No )
3		0sno	|- 0s e. No
4	3	a1i	|- ( ph -> 0s e. No )
5	4 1 2	sltadd2d	|- ( ph -> ( 0s ( B +s 0s )
6	2	addsridd	|- ( ph -> ( B +s 0s ) = B )
7	6	breq1d	|- ( ph -> ( ( B +s 0s ) B
8	5 7	bitrd	|- ( ph -> ( 0s B