Theorem nfsbh | index | src |

theorem nfsbh {x y: nat} (a: nat x y) (b: wff x y):
  $ FN/ x a $ >
  $ F/ x b $ >
  $ F/ x [a / y] b $;
StepHypRefExpression
1 hyp h1
FN/ x a
2 1 nfeq2
F/ x z = a
3 nfv
F/ x y = z
4 hyp h2
F/ x b
5 3, 4 nfim
F/ x y = z -> b
6 5 nfal
F/ x A. y (y = z -> b)
7 2, 6 nfim
F/ x z = a -> A. y (y = z -> b)
8 7 nfal
F/ x A. z (z = a -> A. y (y = z -> b))
9 8 conv sb
F/ x [a / y] 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)