Theorem elSnd | index | src |

theorem elSnd (A: set) (a: nat): $ a e. Snd A <-> b1 a e. A $;
StepHypRefExpression
1 id
_1 = a -> _1 = a
2 1 b1eqd
_1 = a -> b1 _1 = b1 a
3 eqsidd
_1 = a -> A == A
4 2, 3 eleqd
_1 = a -> (b1 _1 e. A <-> b1 a e. A)
5 4 elabe
a e. {_1 | b1 _1 e. A} <-> b1 a e. A
6 5 conv Snd
a e. Snd A <-> b1 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_peano (peano2, addeq)