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Metamath Proof Explorer

Theorem wefr

Description: A well-ordering is well-founded. (Contributed by NM, 22-Apr-1994)

Ref Expression
Assertion wefr ( 𝑅 We 𝐴 → 𝑅 Fr 𝐴 )

Proof

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