Metamath Proof Explorer

Theorem unssad

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

Ref Expression
Hypothesis unssad.1 φ A B C
Assertion unssad φ A C


Step Hyp Ref Expression
1 unssad.1 φ A B C
2 unss A C B C A B C
3 1 2 sylibr φ A C B C
4 3 simpld φ A C