Theorem powereqd | index | src |

theorem powereqd (_G: wff) (_a1 _a2: nat):
  $ _G -> _a1 = _a2 $ >
  $ _G -> power _a1 = power _a2 $;
StepHypRefExpression
1 hyp _ah
_G -> _a1 = _a2
2 1 nseqd
_G -> _a1 == _a2
3 2 Powereqd
_G -> Power _a1 == Power _a2
4 3 lowereqd
_G -> lower (Power _a1) = lower (Power _a2)
5 4 conv power
_G -> power _a1 = power _a2

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)