Theorem eexb ≪ | index | src | ≫ 

theorem eexb {x: nat} (a: wff x) (b: wff): $ E. x a -> b <-> A. x (a -> b) $;
StepHypRefExpression
1 nfex1 
F/ x E. x a
2 nfv 
F/ x b
3 1, 2 nfim 
F/ x E. x a -> b
4 iex 
a -> E. x a
5 4 imim1i 
(E. x a -> b) -> a -> b
6 3, 5 ialdh 
(E. x a -> b) -> A. x (a -> b)
7 nfal1 
F/ x A. x (a -> b)
8 eal 
A. x (a -> b) -> a -> b
9 7, 2, 8 eexdh 
A. x (a -> b) -> E. x a -> b
10 6, 9 ibii 
E. x a -> b <-> A. x (a -> b)

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_12)