Theorem anass ≪ | index | src | ≫ 

theorem anass (a b c: wff): $ a /\ b /\ c <-> a /\ (b /\ c) $;
StepHypRefExpression
1 anll 
a /\ b /\ c -> a
2 anim1 
(a /\ b -> b) -> a /\ b /\ c -> b /\ c
3 anr 
a /\ b -> b
4 2, 3 ax_mp 
a /\ b /\ c -> b /\ c
5 1, 4 iand 
a /\ b /\ c -> a /\ (b /\ c)
6 anim2 
(b /\ c -> b) -> a /\ (b /\ c) -> a /\ b
7 anl 
b /\ c -> b
8 6, 7 ax_mp 
a /\ (b /\ c) -> a /\ b
9 anrr 
a /\ (b /\ c) -> c
10 8, 9 iand 
a /\ (b /\ c) -> a /\ b /\ c
11 5, 10 ibii 
a /\ b /\ c <-> a /\ (b /\ c)

Axiom use

axs_prop_calc (ax_1, ax_2, ax_3, ax_mp)