Theorem elneq2d ≪ | index | src | ≫

theorem elneq2d (G: wff) (a b c: nat):
  $ G -> b = c $ >
  $ G -> (a e. b <-> a e. c) $;

Step	Hyp	Ref	Expression
1		eqidd	G -> a = a
2		hyp h	G -> b = c
3	1, 2	elneqd	G -> (a e. b <-> a e. c)

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)