Theorem applamed2 | index | src |

theorem applamed2 (F: set) (G: wff) (b c: nat) {x: nat} (a: nat x):
  $ G /\ x = b -> a = c $ >
  $ G -> F == \ x, a -> F @ b = c $;
StepHypRefExpression
1 hyp e
G /\ x = b -> a = c
2 1 eqeq2d
G /\ x = b -> (F @ b = a <-> F @ b = c)
3 2 bi1d
G /\ x = b -> F @ b = a -> F @ b = c
4 3 applamed1
G -> F == \ x, a -> F @ b = c

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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)