Theorem receq2 ≪ | index | src | ≫ 

theorem receq2 (z: nat) (_S1 _S2: set) (n: nat):
  $ _S1 == _S2 -> rec z _S1 n = rec z _S2 n $;
StepHypRefExpression
1 id 
_S1 == _S2 -> _S1 == _S2
2 1 receq2d 
_S1 == _S2 -> rec z _S1 n = rec z _S2 n

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)