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

Metamath Proof Explorer

Theorem fvsn

Description: The value of a singleton of an ordered pair is the second member. (Contributed by NM, 12-Aug-1994) (Proof shortened by BJ, 25-Feb-2023)

Ref Expression
Hypotheses fvsn.1 ⊢ A ∈ V
fvsn.2 ⊢ B ∈ V
Assertion fvsn ⊢ A B ⁡ A = B

Proof

Step Hyp Ref Expression
1 fvsn.1 ⊢ A ∈ V
2 fvsn.2 ⊢ B ∈ V
3 fvsng ⊢ A ∈ V ∧ B ∈ V → A B ⁡ A = B
4 1 2 3 mp2an ⊢ A B ⁡ A = B