Theorem sn-ltp1

Description: ltp1 without ax-mulcom . (Contributed by SN, 13-Feb-2024)

	Ref	Expression
Assertion	sn-ltp1	$$⊢A\in ℝ\to A<A+1$$

Proof

Step	Hyp	Ref	Expression
1		1re	$$⊢1\in ℝ$$
2		sn-0lt1	$$⊢0<1$$
3		sn-ltaddpos	$$⊢\left(1\in ℝ\wedge A\in ℝ\right)\to \left(0<1\leftrightarrow A<A+1\right)$$
4	2 3	mpbii	$$⊢\left(1\in ℝ\wedge A\in ℝ\right)\to A<A+1$$
5	1 4	mpan	$$⊢A\in ℝ\to A<A+1$$