Metamath Proof Explorer
		
		
		
		Description:  Define the domain function.  See brdomain for its value.  (Contributed by Scott Fenton, 11-Apr-2014)
		
			
				
					|  |  | Ref | Expression | 
				
					|  | Assertion | df-domain | ⊢  Domain  =  Image ( 1st   ↾  ( V  ×  V ) ) | 
			
		
		
			
				Detailed syntax breakdown
				
					
						| Step | Hyp | Ref | Expression | 
						
							| 0 |  | cdomain | ⊢ Domain | 
						
							| 1 |  | c1st | ⊢ 1st | 
						
							| 2 |  | cvv | ⊢ V | 
						
							| 3 | 2 2 | cxp | ⊢ ( V  ×  V ) | 
						
							| 4 | 1 3 | cres | ⊢ ( 1st   ↾  ( V  ×  V ) ) | 
						
							| 5 | 4 | cimage | ⊢ Image ( 1st   ↾  ( V  ×  V ) ) | 
						
							| 6 | 0 5 | wceq | ⊢ Domain  =  Image ( 1st   ↾  ( V  ×  V ) ) |