Theorem zlteq2d ≪ | index | src | ≫

theorem zlteq2d (_G: wff) (m _n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> (m  m 
    

      

        
Step
Hyp
Ref
Expression
        

          
1
          

          
eqidd
          
_G -> m = m
        
        

          
2
          

          
hyp _h
          
_G -> _n1 = _n2
        
        

          
3
          
1, 2
          
zlteqd
          
_G -> (m <Z _n1 <-> m <Z _n2)
        
      
    
    
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
     (peano2,
      addeq,
      muleq)