Metamath Proof Explorer

Theorem eldifbd

Description: If a class is in the difference of two classes, it is not in the subtrahend. One-way deduction form of eldif . (Contributed by David Moews, 1-May-2017)

Ref Expression
Hypothesis eldifbd.1 φ A B C
Assertion eldifbd φ ¬ A C


Step Hyp Ref Expression
1 eldifbd.1 φ A B C
2 eldif A B C A B ¬ A C
3 1 2 sylib φ A B ¬ A C
4 3 simprd φ ¬ A C