Theorem nfsapp ≪ | index | src | ≫

theorem nfsapp {x: nat} (F: set x) (a: nat x):
  $ FS/ x F $ >
  $ FN/ x a $ >
  $ FS/ x F @@ a $;

Step	Hyp	Ref	Expression
1		hyp h1	FS/ x F
2		hyp h2	FN/ x a
3		nfnv	FN/ x a1
4	2, 3	nfpr	FN/ x a, a1
5	1, 4	nfrapp	FS/ x F @' (a, a1)
6	5	nfsab	FS/ x S\ a1, F @' (a, a1)
7	6	conv sapp	FS/ x F @@ a

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 (peano2, addeq, muleq)