Metamath Proof Explorer

Theorem disjimxrn

Description: Disjointness condition for range Cartesian product. (Contributed by Peter Mazsa, 15-Dec-2020) (Revised by Peter Mazsa, 22-Sep-2021)

Ref Expression
Assertion disjimxrn 
|- ( Disj S -> Disj ( R |X. S ) )

Proof

Step Hyp Ref Expression
1 disjorimxrn 
 |-  ( ( Disj R \/ Disj S ) -> Disj ( R |X. S ) )
2 1 olcs 
 |-  ( Disj S -> Disj ( R |X. S ) )