Theorem aleqe ≪ | index | src | ≫ 

theorem aleqe {x: nat} (a: nat) (p: wff x) (q: wff):
  $ x = a -> (p <-> q) $ >
  $ A. x (x = a -> p) <-> q $;
StepHypRefExpression
1 bitr3 
([a / x] p <-> A. x (x = a -> p)) -> ([a / x] p <-> q) -> (A. x (x = a -> p) <-> q)
2 dfsb2 
[a / x] p <-> A. x (x = a -> p)
3 1, 2 ax_mp 
([a / x] p <-> q) -> (A. x (x = a -> p) <-> q)
4 hyp e 
x = a -> (p <-> q)
5 4 sbe 
[a / x] p <-> q
6 3, 5 ax_mp 
A. x (x = a -> p) <-> q

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)