Metamath Proof Explorer


Theorem wefr

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

Ref Expression
Assertion wefr ( 𝑅 We 𝐴𝑅 Fr 𝐴 )

Proof

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