Theorem sopo 2139

Description: A strict order is a partial order.

Assertion

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

Proof of Theorem sopo

Step	Hyp	Ref	Expression
1		df-so 2138	. 2 |- (R Or A <-> (R Po A /\ A.x e. A A.y e. A (xRy \/ x = y \/ yRx)))
2	1	pm3.26bd 259	1 |- (R Or A -> R Po A)

Syntax hints:   -> wi 2   \/ w3o 580   = weq 797  A.wral 1201   class class class wbr 2054   Po wpo 2058   Or wor 2059

This theorem is referenced by:  sonr 2143  sotr 2144  so2nr 2146  so3nr 2147

This theorem was proved from axioms:  ax-1 3  ax-2 4  ax-3 5  ax-mp 6

This theorem depends on definitions:  df-bi 128  df-an 198  df-so 2138

metamath.org