Theorem ex2len | index | src |

theorem ex2len (R: set) (l1 l2: nat): $ l1, l2 e. ex2 R -> len l1 = len l2 $;
StepHypRefExpression
1 elex2
l1, l2 e. ex2 R <-> len l1 = len l2 /\ E. a1 E. a2 E. a3 (nth a1 l1 = suc a2 /\ nth a1 l2 = suc a3 /\ a2, a3 e. R)
2 anl
len l1 = len l2 /\ E. a1 E. a2 E. a3 (nth a1 l1 = suc a2 /\ nth a1 l2 = suc a3 /\ a2, a3 e. R) -> len l1 = len l2
3 1, 2 sylbi
l1, l2 e. ex2 R -> len l1 = len l2

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 (peano1, peano2, peano5, addeq, muleq, add0, addS, mul0, mulS)