Theorem abid2 | index | src |

theorem abid2 (A: set) {x: nat}: $ {x | x e. A} == A $;
StepHypRefExpression
1 eleq1
x = y -> (x e. A <-> y e. A)
2 1 elabe
y e. {x | x e. A} <-> y e. A
3 2 eqri
{x | x e. A} == A

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)