Theorem zltp1led

Description: Integer ordering relation, a deduction version. (Contributed by metakunt, 23-May-2024)

	Ref	Expression
Hypotheses	zltp1led.1	⊢ ( 𝜑 → 𝑀 ∈ ℤ )
	zltp1led.2	⊢ ( 𝜑 → 𝑁 ∈ ℤ )
Assertion	zltp1led	⊢ ( 𝜑 → ( 𝑀 < 𝑁 ↔ ( 𝑀 + 1 ) ≤ 𝑁 ) )

Proof

Step	Hyp	Ref	Expression
1		zltp1led.1	⊢ ( 𝜑 → 𝑀 ∈ ℤ )
2		zltp1led.2	⊢ ( 𝜑 → 𝑁 ∈ ℤ )
3		zltp1le	⊢ ( ( 𝑀 ∈ ℤ ∧ 𝑁 ∈ ℤ ) → ( 𝑀 < 𝑁 ↔ ( 𝑀 + 1 ) ≤ 𝑁 ) )
4	1 2 3	syl2anc	⊢ ( 𝜑 → ( 𝑀 < 𝑁 ↔ ( 𝑀 + 1 ) ≤ 𝑁 ) )