Proof of proveit.logic.booleans.implication.iff_transitivity theorem

import proveit
theory = proveit.Theory() # the theorem's theory

%proving iff_transitivity

With these allowed/disallowed theorem/theory presumptions (e.g., to avoid circular dependencies), we begin our proof of
iff_transitivity:
(see dependencies)

iff_transitivity.instance_expr.prove(assumptions=iff_transitivity.conditions)

,  ⊢  

iff_transitivity may now be readily provable (assuming required theorems are usable).  Simply execute "%qed".

%qed # automation can handle this

proveit.logic.booleans.implication.iff_transitivity has been proven.

	step type	requirements	statement
0	generalization	1	⊢
1	instantiation	2, 3, 4	,  ⊢
	: , :
2	theorem		⊢
	proveit.logic.booleans.implication.iff_intro
3	deduction	5	,  ⊢
4	deduction	6	,  ⊢
5	modus ponens	7, 8	, ,  ⊢
6	modus ponens	9, 10	, ,  ⊢
7	instantiation	15, 18	⊢
	: , :
8	modus ponens	11, 12	,  ⊢
9	instantiation	17, 16	⊢
	: , :
10	modus ponens	13, 14	,  ⊢
11	instantiation	15, 16	⊢
	: , :
12	assumption		⊢
13	instantiation	17, 18	⊢
	: , :
14	assumption		⊢
15	theorem		⊢
	proveit.logic.booleans.implication.iff_implies_right
16	assumption		⊢
17	theorem		⊢
	proveit.logic.booleans.implication.iff_implies_left
18	assumption		⊢