Metamath Proof Explorer

Theorem unissd

Description: Subclass relationship for subclass union. Deduction form of uniss . (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypothesis unissd.1 
|- ( ph -> A C_ B )
Assertion unissd 
|- ( ph -> U. A C_ U. B )

Proof

Step Hyp Ref Expression
1 unissd.1 
 |-  ( ph -> A C_ B )
2 uniss 
 |-  ( A C_ B -> U. A C_ U. B )
3 1 2 syl 
 |-  ( ph -> U. A C_ U. B )