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Metamath Proof Explorer

Theorem weso

Description: A well-ordering is a strict ordering. (Contributed by NM, 16-Mar-1997)

Ref Expression
Assertion weso ( 𝑅 We 𝐴 → 𝑅 Or 𝐴 )

Proof

Step Hyp Ref Expression
1 df-we ⊢ ( 𝑅 We 𝐴 ↔ ( 𝑅 Fr 𝐴 ∧ 𝑅 Or 𝐴 ) )
2 1 simprbi ⊢ ( 𝑅 We 𝐴 → 𝑅 Or 𝐴 )