Theorem nn0p1gt0

Description: A nonnegative integer increased by 1 is greater than 0. (Contributed by Alexander van der Vekens, 3-Oct-2018)

	Ref	Expression
Assertion	nn0p1gt0	⊢ ( 𝑁 ∈ ℕ0 → 0 < ( 𝑁 + 1 ) )

Proof

Step	Hyp	Ref	Expression
1		nn0re	⊢ ( 𝑁 ∈ ℕ0 → 𝑁 ∈ ℝ )
2		1red	⊢ ( 𝑁 ∈ ℕ0 → 1 ∈ ℝ )
3		nn0ge0	⊢ ( 𝑁 ∈ ℕ0 → 0 ≤ 𝑁 )
4		0lt1	⊢ 0 < 1
5	4	a1i	⊢ ( 𝑁 ∈ ℕ0 → 0 < 1 )
6	1 2 3 5	addgegt0d	⊢ ( 𝑁 ∈ ℕ0 → 0 < ( 𝑁 + 1 ) )