Theorem apprlamed ≪ | index | src | ≫

theorem apprlamed (G: wff) (a c d: nat) {x: nat} (b: nat x):
  $ G /\ x = c -> b = d $ >
  $ G -> c e. a $ >
  $ G -> (\. x e. a, b) @ c = d $;

Step	Hyp	Ref	Expression
1		apprlams	c e. a -> (\. x e. a, b) @ c = N[c / x] b
2		hyp h	G -> c e. a
3	1, 2	syl	G -> (\. x e. a, b) @ c = N[c / x] b
4		hyp e	G /\ x = c -> b = d
5	4	sbned	G -> N[c / x] b = d
6	3, 5	eqtrd	G -> (\. 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)