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Metamath Proof Explorer

Theorem 1nq

Description: The positive fraction 'one'. (Contributed by NM, 29-Oct-1995) (Revised by Mario Carneiro, 28-Apr-2013) (New usage is discouraged.)

Ref Expression
Assertion 1nq 1Q ∈ Q

Proof

Step Hyp Ref Expression
1 df-1nq ⊢ 1Q = ⟨ 1o , 1o ⟩
2 1pi ⊢ 1o ∈ N
3 pinq ⊢ ( 1o ∈ N → ⟨ 1o , 1o ⟩ ∈ Q )
4 2 3 ax-mp ⊢ ⟨ 1o , 1o ⟩ ∈ Q
5 1 4 eqeltri ⊢ 1Q ∈ Q