Theorem sbth | index | src |

theorem sbth {x: nat} (a: nat x) (p: wff x): $ p $ > $ [a / x] p $;
StepHypRefExpression
1 hyp h
p
2 1 a1i
x = y -> p
3 2 ax_gen
A. x (x = y -> p)
4 3 a1i
y = a -> A. x (x = y -> p)
5 4 ax_gen
A. y (y = a -> A. x (x = y -> p))
6 5 conv sb
[a / x] p

Axiom use

axs_prop_calc (ax_1, ax_mp), axs_pred_calc (ax_gen)