Theorem sn-ltp1

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

	Ref	Expression
Assertion	sn-ltp1	|- ( A e. RR -> A < ( A + 1 ) )

Proof

Step	Hyp	Ref	Expression
1		1re	|- 1 e. RR
2		sn-0lt1	|- 0 < 1
3		sn-ltaddpos	|- ( ( 1 e. RR /\ A e. RR ) -> ( 0 < 1 <-> A < ( A + 1 ) ) )
4	2 3	mpbii	|- ( ( 1 e. RR /\ A e. RR ) -> A < ( A + 1 ) )
5	1 4	mpan	|- ( A e. RR -> A < ( A + 1 ) )