Theorem sbeh | index | src |

theorem sbeh {x: nat} (a: nat) (b c: wff x):
  $ F/ x c $ >
  $ x = a -> (b <-> c) $ >
  $ [a / x] b <-> c $;
StepHypRefExpression
1 hyp h
F/ x c
2 1 sbeht
A. x (x = a -> (b <-> c)) -> ([a / x] b <-> c)
3 hyp e
x = a -> (b <-> c)
4 3 ax_gen
A. x (x = a -> (b <-> c))
5 2, 4 ax_mp
[a / x] b <-> c

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)