Theorem elabe ≪ | index | src | ≫ 

theorem elabe {x: nat} (a: nat) (p: wff x) (q: wff):
  $ x = a -> (p <-> q) $ >
  $ a e. {x | p} <-> q $;
StepHypRefExpression
1 bitr 
(a e. {x | p} <-> [a / x] p) -> ([a / x] p <-> q) -> (a e. {x | p} <-> q)
2 elab2 
a e. {x | p} <-> [a / x] p
3 1, 2 ax_mp 
([a / x] p <-> q) -> (a e. {x | p} <-> q)
4 hyp e 
x = a -> (p <-> q)
5 4 sbe 
[a / x] p <-> q
6 3, 5 ax_mp 
a e. {x | 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), axs_set (elab, ax_8)