Theorem wefr 4503

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

Assertion

Ref	Expression
wefr	|- ( R We A -> R Fr A )

Proof of Theorem wefr

Dummy variables x y z are mutually distinct and distinct from all other variables.

Step	Hyp	Ref	Expression
1		df-wetr 4479	. 2 |- ( R We A <-> ( R Fr A /\ A. x e. A A. y e. A A. z e. A ( ( x R y /\ y R z ) -> x R z ) ) )
2	1	simplbi 274	1 |- ( R We A -> R Fr A )

This proof depends on syntax axioms:   -> wi 4   /\ wa 104   A.wral 2528   class class class wbr 4130   Fr wfr 4473   We wwe 4475

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-ia1 106

This proof depends on definitions:  df-bi 117  df-wetr 4479

This theorem is used by:  wepo  4504  wetriext  4724