Metamath Proof Explorer
		
		
		
		Description:  Equality inference for operation value.  (Contributed by FL, 11-Jul-2010)
		
			
				
					|  |  | Ref | Expression | 
					
						|  | Hypotheses | oveq123i.1 | |- A = C | 
					
						|  |  | oveq123i.2 | |- B = D | 
					
						|  |  | oveq123i.3 | |- F = G | 
				
					|  | Assertion | oveq123i | |- ( A F B ) = ( C G D ) | 
			
		
		
			
				Proof
				
					
						| Step | Hyp | Ref | Expression | 
						
							| 1 |  | oveq123i.1 |  |-  A = C | 
						
							| 2 |  | oveq123i.2 |  |-  B = D | 
						
							| 3 |  | oveq123i.3 |  |-  F = G | 
						
							| 4 | 1 2 | oveq12i |  |-  ( A F B ) = ( C F D ) | 
						
							| 5 | 3 | oveqi |  |-  ( C F D ) = ( C G D ) | 
						
							| 6 | 4 5 | eqtri |  |-  ( A F B ) = ( C G D ) |