Description: The intersection of the empty set with a class is the empty set. (Contributed by Glauco Siliprandi, 17-Aug-2020)
Ref | Expression | ||
---|---|---|---|
Assertion | 0in | ⊢ ( ∅ ∩ 𝐴 ) = ∅ |
Step | Hyp | Ref | Expression |
---|---|---|---|
1 | incom | ⊢ ( ∅ ∩ 𝐴 ) = ( 𝐴 ∩ ∅ ) | |
2 | in0 | ⊢ ( 𝐴 ∩ ∅ ) = ∅ | |
3 | 1 2 | eqtri | ⊢ ( ∅ ∩ 𝐴 ) = ∅ |