Theorem nfmul ≪ | index | src | ≫

theorem nfmul {x: nat} (a b: nat x):
  $ FN/ x a $ >
  $ FN/ x b $ >
  $ FN/ x a * b $;

Step	Hyp	Ref	Expression
1		anl	y = a /\ z = b -> y = a
2		anr	y = a /\ z = b -> z = b
3	1, 2	muleqd	y = a /\ z = b -> y * z = a * b
4		hyp h1	FN/ x a
5		hyp h2	FN/ x b
6	3, 4, 5	nfnlem2	FN/ x a * 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 (muleq)