Theorem rappeq | index | src |

theorem rappeq (_F1 _F2: set) (_x1 _x2: nat):
  $ _F1 == _F2 -> _x1 = _x2 -> _F1 @' _x1 == _F2 @' _x2 $;
StepHypRefExpression
1 anl
_F1 == _F2 /\ _x1 = _x2 -> _F1 == _F2
2 anr
_F1 == _F2 /\ _x1 = _x2 -> _x1 = _x2
3 1, 2 rappeqd
_F1 == _F2 /\ _x1 = _x2 -> _F1 @' _x1 == _F2 @' _x2
4 3 exp
_F1 == _F2 -> _x1 = _x2 -> _F1 @' _x1 == _F2 @' _x2

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)