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 |