Theorem unssbd

Description: If ( A u. B ) is contained in C , so is B . One-way deduction form of unss . Partial converse of unssd . (Contributed by David Moews, 1-May-2017)

	Ref	Expression
Hypothesis	unssad.1	|- ( ph -> ( A u. B ) C_ C )
Assertion	unssbd	|- ( ph -> B C_ C )

Proof

Step	Hyp	Ref	Expression
1		unssad.1	|- ( ph -> ( A u. B ) C_ C )
2		unss	|- ( ( A C_ C /\ B C_ C ) <-> ( A u. B ) C_ C )
3	1 2	sylibr	|- ( ph -> ( A C_ C /\ B C_ C ) )
4	3	simprd	|- ( ph -> B C_ C )