Theorem nfsb1 | index | src |

theorem nfsb1 {x: nat} (a: nat) (b: wff x): $ F/ x [a / x] b $;
StepHypRefExpression
1 nfv
F/ x y = a
2 nfal1
F/ x A. x (x = y -> b)
3 1, 2 nfim
F/ x y = a -> A. x (x = y -> b)
4 3 nfal
F/ x A. y (y = a -> A. x (x = y -> b))
5 4 conv sb
F/ x [a / x] 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)