This is an inofficial mirror of http://metamath.tirix.org for personal testing of a visualizer extension only.

Metamath Proof Explorer

Theorem brvdif2

Description: Binary relation with universal complement. (Contributed by Peter Mazsa, 14-Jul-2018)

Ref Expression
Assertion brvdif2 ⊢ A V ∖ R B ↔ ¬ A B ∈ R

Proof

Step Hyp Ref Expression
1 brvdif ⊢ A V ∖ R B ↔ ¬ A R B
2 df-br ⊢ A R B ↔ A B ∈ R
3 1 2 xchbinx ⊢ A V ∖ R B ↔ ¬ A B ∈ R