Metamath Proof Explorer


Theorem elprnq

Description: A positive real is a set of positive fractions. (Contributed by NM, 13-Mar-1996) (Revised by Mario Carneiro, 11-May-2013) (New usage is discouraged.)

Ref Expression
Assertion elprnq
|- ( ( A e. P. /\ B e. A ) -> B e. Q. )

Proof

Step Hyp Ref Expression
1 prpssnq
 |-  ( A e. P. -> A C. Q. )
2 1 pssssd
 |-  ( A e. P. -> A C_ Q. )
3 2 sselda
 |-  ( ( A e. P. /\ B e. A ) -> B e. Q. )