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Metamath Proof Explorer

Theorem relsnop

Description: A singleton of an ordered pair is a relation. (Contributed by NM, 17-May-1998) (Revised by Mario Carneiro, 26-Apr-2015)

Ref Expression
Hypotheses relsn.1 ⊢ A ∈ V
relsnop.2 ⊢ B ∈ V
Assertion relsnop ⊢ Rel ⁡ A B

Proof

Step Hyp Ref Expression
1 relsn.1 ⊢ A ∈ V
2 relsnop.2 ⊢ B ∈ V
3 relsnopg ⊢ A ∈ V ∧ B ∈ V → Rel ⁡ A B
4 1 2 3 mp2an ⊢ Rel ⁡ A B