Metamath Proof Explorer

Theorem brresi

Description: Binary relation on a restriction. (Contributed by NM, 12-Dec-2006)

Ref Expression
Hypothesis opelresi.1 ⊢ C ∈ V
Assertion brresi ⊢ B R ↾ A C ↔ B ∈ A ∧ B R C

Proof

Step Hyp Ref Expression
1 opelresi.1 ⊢ C ∈ V
2 brres ⊢ C ∈ V → B R ↾ A C ↔ B ∈ A ∧ B R C
3 1 2 ax-mp ⊢ B R ↾ A C ↔ B ∈ A ∧ B R C