Theorem eqrlam ≪ | index | src | ≫ 

theorem eqrlam (a f: nat) {x: nat} (b: nat x):
  $ f = \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = b) $;
StepHypRefExpression
1 bitr3 
(f == \. x e. a, b <-> f = \. x e. a, b) ->
  (f == \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = b)) ->
  (f = \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = b))
2 nsinj 
f == \. x e. a, b <-> f = \. x e. a, b
3 1, 2 ax_mp 
(f == \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = b)) -> (f = \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = b))
4 eqsrlam 
f == \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = b)
5 3, 4 ax_mp 
f = \. x e. a, b <-> isfun f /\ Dom f == a /\ A. x (x e. a -> f @ x = 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)