Theorem elneqd | index | src |

theorem elneqd (G: wff) (a b c d: nat):
  $ G -> a = b $ >
  $ G -> c = d $ >
  $ G -> (a e. c <-> b e. d) $;
StepHypRefExpression
1 hyp h1
G -> a = b
2 hyp h2
G -> c = d
3 2 nseqd
G -> c == d
4 1, 3 eleqd
G -> (a e. c <-> b e. 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 (peano2, addeq, muleq)