This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem sn-ltp1

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

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

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