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Metamath Proof Explorer

Theorem ecelqsi

Description: Membership of an equivalence class in a quotient set. (Contributed by NM, 25-Jul-1995) (Revised by Mario Carneiro, 9-Jul-2014)

Ref Expression
Hypothesis ecelqsi.1 ⊢ R ∈ V
Assertion ecelqsi ⊢ B ∈ A → B R ∈ A / R

Proof

Step Hyp Ref Expression
1 ecelqsi.1 ⊢ R ∈ V
2 ecelqsw ⊢ R ∈ V ∧ B ∈ A → B R ∈ A / R
3 1 2 mpan ⊢ B ∈ A → B R ∈ A / R