Metamath Proof Explorer

Theorem bnj931

Description: First-order logic and set theory. (Contributed by Jonathan Ben-Naim, 3-Jun-2011) (New usage is discouraged.)

Ref Expression
Hypothesis bnj931.1 
|- A = ( B u. C )
Assertion bnj931 
|- B C_ A

Proof

Step Hyp Ref Expression
1 bnj931.1 
 |-  A = ( B u. C )
2 ssun1 
 |-  B C_ ( B u. C )
3 2 1 sseqtrri 
 |-  B C_ A