Theorem pi21pr | index | src |

theorem pi21pr (a b c: nat): $ pi21 (a, b, c) = b $;
StepHypRefExpression
1 eqtr
pi21 (a, b, c) = fst (b, c) -> fst (b, c) = b -> pi21 (a, b, c) = b
2 fsteq
snd (a, b, c) = b, c -> fst (snd (a, b, c)) = fst (b, c)
3 2 conv pi21
snd (a, b, c) = b, c -> pi21 (a, b, c) = fst (b, c)
4 sndpr
snd (a, b, c) = b, c
5 3, 4 ax_mp
pi21 (a, b, c) = fst (b, c)
6 1, 5 ax_mp
fst (b, c) = b -> pi21 (a, b, c) = b
7 fstpr
fst (b, c) = b
8 6, 7 ax_mp
pi21 (a, b, c) = b

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)