Theorem cpl0 | index | src |

theorem cpl0: $ Compl 0 == _V $;
StepHypRefExpression
1 eqstr3
Compl (Compl _V) == Compl 0 -> Compl (Compl _V) == _V -> Compl 0 == _V
2 cpleq
Compl _V == 0 -> Compl (Compl _V) == Compl 0
3 cplv
Compl _V == 0
4 2, 3 ax_mp
Compl (Compl _V) == Compl 0
5 1, 4 ax_mp
Compl (Compl _V) == _V -> Compl 0 == _V
6 cplcpl
Compl (Compl _V) == _V
7 5, 6 ax_mp
Compl 0 == _V

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)