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theorem exeqe {x: nat} (a: nat) (p: wff x) (q: wff):
  $ x = a -> (p <-> q) $ >
  $ E. x (x = a /\ p) <-> q $;
StepHypRefExpression
1 bitr3 
([a / x] p <-> E. x (x = a /\ p)) -> ([a / x] p <-> q) -> (E. x (x = a /\ p) <-> q)
2 dfsb3 
[a / x] p <-> E. x (x = a /\ p)
3 1, 2 ax_mp 
([a / x] p <-> q) -> (E. x (x = a /\ p) <-> q)
4 hyp e 
x = a -> (p <-> q)
5 4 sbe 
[a / x] p <-> q
6 3, 5 ax_mp 
E. 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)