Theorem isf0 | index | src |

theorem isf0: $ isfun 0 $;
StepHypRefExpression
1 absurd
~x, y e. 0 -> x, y e. 0 -> x, z e. 0 -> y = z
2 el02
~x, y e. 0
3 1, 2 ax_mp
x, y e. 0 -> x, z e. 0 -> y = z
4 3 ax_gen
A. z (x, y e. 0 -> x, z e. 0 -> y = z)
5 4 ax_gen
A. y A. z (x, y e. 0 -> x, z e. 0 -> y = z)
6 5 ax_gen
A. x A. y A. z (x, y e. 0 -> x, z e. 0 -> y = z)
7 6 conv isfun
isfun 0

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)