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Metamath Proof Explorer

Theorem lem1d

Description: A number minus 1 is less than or equal to itself. (Contributed by Mario Carneiro, 28-May-2016)

		Ref	Expression
	Hypothesis	ltp1d.1	$⊢ φ \to A \in ℝ$
	Assertion	lem1d	$⊢ φ \to A - 1 \leq A$

Step	Hyp	Ref	Expression
1		ltp1d.1	$⊢ φ \to A \in ℝ$
2		lem1	$⊢ A \in ℝ \to A - 1 \leq A$
3	1 2	syl	$⊢ φ \to A - 1 \leq A$