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Metamath Proof Explorer

Theorem opi2

Description: One of the two elements of an ordered pair. (Contributed by NM, 5-Aug-1993) (Revised by Mario Carneiro, 26-Apr-2015) (Avoid depending on this detail.)

Ref Expression
Hypotheses opi1.1 ⊢ A ∈ V
opi1.2 ⊢ B ∈ V
Assertion opi2 ⊢ A B ∈ A B

Proof

Step Hyp Ref Expression
1 opi1.1 ⊢ A ∈ V
2 opi1.2 ⊢ B ∈ V
3 prex ⊢ A B ∈ V
4 3 prid2 ⊢ A B ∈ A A B
5 1 2 dfop ⊢ A B = A A B
6 4 5 eleqtrri ⊢ A B ∈ A B