Theorem elrn | index | src |

theorem elrn (A: set) (a: nat) {x: nat}: $ a e. Ran A <-> E. x x, a e. A $;
StepHypRefExpression
1 preq2
y = a -> x, y = x, a
2 1 eleq1d
y = a -> (x, y e. A <-> x, a e. A)
3 2 exeqd
y = a -> (E. x x, y e. A <-> E. x x, a e. A)
4 3 elabe
a e. {y | E. x x, y e. A} <-> E. x x, a e. A
5 4 conv Ran
a e. Ran A <-> E. x x, a e. 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), axs_the (theid, the0), axs_peano (peano2, addeq, muleq)