Theorem apprlame | index | src |

theorem apprlame (a c d: nat) {x: nat} (b: nat x):
  $ x = c -> b = d $ >
  $ c e. a -> (\. x e. a, b) @ c = d $;
StepHypRefExpression
1 hyp e
x = c -> b = d
2 1 sbne
N[c / x] b = d
3 apprlams
c e. a -> (\. x e. a, b) @ c = N[c / x] b
4 2, 3 syl6eq
c e. a -> (\. x e. a, b) @ c = d

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)