Theorem Ifpos | index | src |

theorem Ifpos (A B: set) (p: wff): $ p -> If p A B == A $;
StepHypRefExpression
1 ifppos
p -> (ifp p (n e. A) (n e. B) <-> n e. A)
2 1 eqab1d
p -> {n | ifp p (n e. A) (n e. B)} == A
3 2 conv If
p -> If p A B == 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)