theorem addeq2 (a _b1 _b2: nat): $ _b1 = _b2 -> a + _b1 = a + _b2 $;
    
      
        | Step | Hyp | Ref | Expression | 
|---|
        
          | 1 |  | id | _b1 = _b2 -> _b1 = _b2 | 
        
          | 2 | 1 | addeq2d | _b1 = _b2 -> a + _b1 = a + _b2 | 
      
    
    Axiom use
    axs_prop_calc
     (ax_1,
      ax_2,
      ax_3,
      ax_mp),
    
axs_pred_calc
     (ax_gen,
      ax_4,
      ax_5,
      ax_6,
      ax_7),
    
axs_peano
     (addeq)