Metamath Proof Explorer
		
		
		
		Description:  An upper integer is an extended real.  (Contributed by Glauco
       Siliprandi, 2-Jan-2022)
		
			
				
					|  |  | Ref | Expression | 
					
						|  | Hypotheses | uzxrd.1 | |- Z = ( ZZ>= ` M ) | 
					
						|  |  | uzxrd.2 | |- ( ph -> A e. Z ) | 
				
					|  | Assertion | uzxrd | |- ( ph -> A e. RR* ) | 
			
		
		
			
				Proof
				
					
						| Step | Hyp | Ref | Expression | 
						
							| 1 |  | uzxrd.1 |  |-  Z = ( ZZ>= ` M ) | 
						
							| 2 |  | uzxrd.2 |  |-  ( ph -> A e. Z ) | 
						
							| 3 |  | ressxr |  |-  RR C_ RR* | 
						
							| 4 | 1 2 | uzred |  |-  ( ph -> A e. RR ) | 
						
							| 5 | 3 4 | sselid |  |-  ( ph -> A e. RR* ) |