Theorem nfsb | index | src |

theorem nfsb {x y: nat} (a: nat y) (b: wff x y):
  $ F/ x b $ >
  $ F/ x [a / y] b $;
StepHypRefExpression
1 nfv
F/ x z = a
2 nfv
F/ x y = z
3 hyp h
F/ x b
4 2, 3 nfim
F/ x y = z -> b
5 4 nfal
F/ x A. y (y = z -> b)
6 1, 5 nfim
F/ x z = a -> A. y (y = z -> b)
7 6 nfal
F/ x A. z (z = a -> A. y (y = z -> b))
8 7 conv sb
F/ x [a / y] b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_11, ax_12)