Theorem appneq1d ≪ | index | src | ≫

theorem appneq1d (G: wff) (f g x: nat): $ G -> f = g $ > $ G -> f @ x = g @ x $;

Step	Hyp	Ref	Expression
1		hyp h	G -> f = g
2	1	nseqd	G -> f == g
3	2	appeq1d	G -> f @ x = g @ x

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)