Theorem rlamArrow | index | src |

theorem rlamArrow (B: set) (a: nat) {x: nat} (b: nat x):
  $ \. x e. a, b e. Arrow a B <-> A. x (x e. a -> b e. B) $;
StepHypRefExpression
1 bitr
(\. x e. a, b e. Arrow a B <-> func (\. x e. a, b) a B) ->
  (func (\. x e. a, b) a B <-> A. x (x e. a -> b e. B)) ->
  (\. x e. a, b e. Arrow a B <-> A. x (x e. a -> b e. B))
2 elArrow
\. x e. a, b e. Arrow a B <-> func (\. x e. a, b) a B
3 1, 2 ax_mp
(func (\. x e. a, b) a B <-> A. x (x e. a -> b e. B)) -> (\. x e. a, b e. Arrow a B <-> A. x (x e. a -> b e. B))
4 rlamfunc
func (\. x e. a, b) a B <-> A. x (x e. a -> b e. B)
5 3, 4 ax_mp
\. x e. a, b e. Arrow a B <-> A. x (x e. a -> b e. B)

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)