Theorem sopo

Description: A strict linear order is a strict partial order. (Contributed by NM, 28-Mar-1997)

	Ref	Expression
Assertion	sopo	⊢ ( 𝑅 Or 𝐴 → 𝑅 Po 𝐴 )

Proof

Step	Hyp	Ref	Expression
1		df-so	⊢ ( 𝑅 Or 𝐴 ↔ ( 𝑅 Po 𝐴 ∧ ∀ 𝑥 ∈ 𝐴 ∀ 𝑦 ∈ 𝐴 ( 𝑥 𝑅 𝑦 ∨ 𝑥 = 𝑦 ∨ 𝑦 𝑅 𝑥 ) ) )
2	1	simplbi	⊢ ( 𝑅 Or 𝐴 → 𝑅 Po 𝐴 )