Theorem zleeqd | index | src |

theorem zleeqd (_G: wff) (_m1 _m2 _n1 _n2: nat):
  $ _G -> _m1 = _m2 $ >
  $ _G -> _n1 = _n2 $ >
  $ _G -> (_m1 <=Z _n1 <-> _m2 <=Z _n2) $;
StepHypRefExpression
1 hyp _nh
_G -> _n1 = _n2
2 hyp _mh
_G -> _m1 = _m2
3 1, 2 zlteqd
_G -> (_n1 <Z _m1 <-> _n2 <Z _m2)
4 3 noteqd
_G -> (~_n1 <Z _m1 <-> ~_n2 <Z _m2)
5 4 conv zle
_G -> (_m1 <=Z _n1 <-> _m2 <=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)