Theorem nfim ≪ | index | src | ≫ 

theorem nfim {x: nat} (a b: wff x): $ F/ x a $ > $ F/ x b $ > $ F/ x a -> b $;
StepHypRefExpression
1 ax_1 
b -> a -> b
2 1 alimi 
A. x b -> A. x (a -> b)
3 hyp h2 
F/ x b
4 3 nfi 
b -> A. x b
5 2, 4 syl 
b -> A. x (a -> b)
6 mpcom 
a -> (a -> b) -> b
7 5, 6 syl6 
a -> (a -> b) -> A. x (a -> b)
8 absurd 
~a -> a -> b
9 8 alimi 
A. x ~a -> A. x (a -> b)
10 hyp h1 
F/ x a
11 10 nfnot 
F/ x ~a
12 11 nfi 
~a -> A. x ~a
13 9, 12 syl 
~a -> A. x (a -> b)
14 13 a1d 
~a -> (a -> b) -> A. x (a -> b)
15 7, 14 cases 
(a -> b) -> A. x (a -> b)
16 15 nfri 
F/ x a -> b

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp), axs_pred_calc (ax_gen, ax_4, ax_5, ax_6, ax_7, ax_10, ax_12)