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 𝐴𝑅 Or 𝐴 )

Proof

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