Theorem resv | index | src |

theorem resv (F: set): $ F |` _V == F $;
StepHypRefExpression
1 eqstr
F |` _V == F i^i _V -> F i^i _V == F -> F |` _V == F
2 ineq2
Xp _V _V == _V -> F i^i Xp _V _V == F i^i _V
3 2 conv res
Xp _V _V == _V -> F |` _V == F i^i _V
4 xpvv
Xp _V _V == _V
5 3, 4 ax_mp
F |` _V == F i^i _V
6 1, 5 ax_mp
F i^i _V == F -> F |` _V == F
7 inv2
F i^i _V == F
8 6, 7 ax_mp
F |` _V == F

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)