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

Metamath Proof Explorer

Theorem brco

Description: Binary relation on a composition. (Contributed by NM, 21-Sep-2004) (Revised by Mario Carneiro, 24-Feb-2015)

Ref Expression
Hypotheses opelco.1 ⊢ A ∈ V
opelco.2 ⊢ B ∈ V
Assertion brco ⊢ A C ∘ D B ↔ ∃ x A D x ∧ x C B

Proof

Step Hyp Ref Expression
1 opelco.1 ⊢ A ∈ V
2 opelco.2 ⊢ B ∈ V
3 brcog ⊢ A ∈ V ∧ B ∈ V → A C ∘ D B ↔ ∃ x A D x ∧ x C B
4 1 2 3 mp2an ⊢ A C ∘ D B ↔ ∃ x A D x ∧ x C B