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

import proveit
from proveit import defaults
from proveit import B
from proveit.logic import Not
theory = proveit.Theory() # the theorem's theory

%proving contrapose_neg_antecedent

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

defaults.assumptions = list(contrapose_neg_antecedent.all_conditions()) + [Not(B)]

defaults.assumptions:

not_a_implies_B = defaults.assumptions[0]

not_a_implies_B:

not_a_implies_B.deny_antecedent().as_implication(Not(B))

,  ⊢  

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

%qed

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

	step type	requirements	statement
0	generalization	1	⊢
1	deduction	2	,  ⊢
2	instantiation	3, 4, 5, 6	, ,  ⊢
	:
3	conjecture		⊢
	proveit.logic.booleans.implication.modus_tollens_affirmation
4	assumption		⊢
5	assumption		⊢
6	assumption		⊢