Theorem sopo 4458

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 4442	. 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 4130   Po wpo 4439   Or wor 4440

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 4442

This theorem is used by:  sonr  4462  sotr  4463  so2nr  4466  so3nr  4467  sosng  4848  fimaxq  11270