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 ∧ ∀x ∈ A ∀y ∈ 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  ∀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

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