Theorem pi21eqd | index | src |

theorem pi21eqd (_G: wff) (_n1 _n2: nat):
  $ _G -> _n1 = _n2 $ >
  $ _G -> pi21 _n1 = pi21 _n2 $;
StepHypRefExpression
1 hyp _nh
_G -> _n1 = _n2
2 1 sndeqd
_G -> snd _n1 = snd _n2
3 2 fsteqd
_G -> fst (snd _n1) = fst (snd _n2)
4 3 conv pi21
_G -> pi21 _n1 = pi21 _n2

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)