Theorem zlttr ≪ | index | src | ≫

theorem zlttr (a b c: nat): $ a  b  a 
    

      

        
Step
Hyp
Ref
Expression
        

          
1
          

          
zlelttr
          
a <=Z b -> b <Z c -> a <Z c
        
        

          
2
          

          
zltle
          
a <Z b -> a <=Z b
        
        

          
3
          
1, 2
          
syl
          
a <Z b -> b <Z c -> a <Z c
        
      
    
    
Axiom use
    axs_prop_calc
     (ax_1,
      ax_2,
      ax_3,
      ax_mp,
      itru),
    axs_pred_calc
     (ax_gen,
      ax_4,
      ax_5,
      ax_6,
      ax_7,
      ax_10,
      ax_11,
      ax_12),
    axs_set
     (elab,
      ax_8),
    axs_the
     (theid,
      the0),
    axs_peano
     (peano1,
      peano2,
      peano5,
      addeq,
      muleq,
      add0,
      addS,
      mul0,
      mulS)