Theorem ltm1d

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

	Ref	Expression
Hypothesis	ltp1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
Assertion	ltm1d	⊢ ( 𝜑 → ( 𝐴 − 1 ) < 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		ltp1d.1	⊢ ( 𝜑 → 𝐴 ∈ ℝ )
2		ltm1	⊢ ( 𝐴 ∈ ℝ → ( 𝐴 − 1 ) < 𝐴 )
3	1 2	syl	⊢ ( 𝜑 → ( 𝐴 − 1 ) < 𝐴 )