Theorem sopo 4460

Description: A strict linear order is a strict partial order. (Contributed by NM, 28-Mar-1997.)

Assertion

Ref	Expression
sopo	|- ( R Or A -> R Po A )

Proof of Theorem sopo

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

Step	Hyp	Ref	Expression
1		df-iso 4444	. 2 |- ( R Or A <-> ( R Po A /\ A. x e. A A. y e. A A. z e. A ( x R y -> ( x R z \/ z R y ) ) ) )
2	1	simplbi 274	1 |- ( R Or A -> R Po A )

This proof depends on syntax axioms:   -> wi 4   \/ wo 720   A.wral 2528   class class class wbr 4131   Po wpo 4441   Or wor 4442

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-iso 4444

This theorem is used by:  sonr  4464  sotr  4465  so2nr  4468  so3nr  4469  sosng  4850  fimaxq  11292