Theorem sltsubposd

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

	Ref	Expression
Hypotheses	sltsubpos.1	$$⊢\phi \to A\in \mathrm{No}$$
	sltsubpos.2	$$⊢\phi \to B\in \mathrm{No}$$
Assertion	sltsubposd	Could not format assertion : No typesetting found for |- ( ph -> ( 0s ( B -s A )

Proof

Step	Hyp	Ref	Expression
1		sltsubpos.1	$$⊢\phi \to A\in \mathrm{No}$$
2		sltsubpos.2	$$⊢\phi \to B\in \mathrm{No}$$
3		0sno	Could not format 0s e. No : No typesetting found for |- 0s e. No with typecode |-
4	3	a1i	Could not format ( ph -> 0s e. No ) : No typesetting found for |- ( ph -> 0s e. No ) with typecode |-
5	4 1 2	sltsub2d	Could not format ( ph -> ( 0s ( B -s A ) ( 0s ( B -s A )
6		subsid1	Could not format ( B e. No -> ( B -s 0s ) = B ) : No typesetting found for |- ( B e. No -> ( B -s 0s ) = B ) with typecode |-
7	2 6	syl	Could not format ( ph -> ( B -s 0s ) = B ) : No typesetting found for |- ( ph -> ( B -s 0s ) = B ) with typecode |-
8	7	breq2d	Could not format ( ph -> ( ( B -s A ) ( B -s A ) ( ( B -s A ) ( B -s A )
9	5 8	bitrd	Could not format ( ph -> ( 0s ( B -s A ) ( 0s ( B -s A )