Nuprl Lemma : triple-neg
∀[A:ℙ]. uiff(¬¬¬A;¬A)
Proof
Definitions occuring in Statement : 
uiff: uiff(P;Q)
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
not: ¬A
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
not: ¬A
, 
implies: P 
⇒ Q
, 
false: False
, 
decidable: Dec(P)
, 
or: P ∨ Q
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
dneg_elim_a, 
not_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
independent_pairFormation, 
lambdaFormation, 
thin, 
hypothesis, 
sqequalHypSubstitution, 
independent_functionElimination, 
extract_by_obid, 
isectElimination, 
hypothesisEquality, 
inlFormation, 
productElimination, 
promote_hyp, 
voidElimination, 
sqequalRule, 
lambdaEquality, 
dependent_functionElimination, 
because_Cache, 
addLevel, 
impliesFunctionality, 
independent_pairEquality, 
isect_memberEquality, 
equalityTransitivity, 
equalitySymmetry, 
universeEquality
Latex:
\mforall{}[A:\mBbbP{}].  uiff(\mneg{}\mneg{}\mneg{}A;\mneg{}A)
Date html generated:
2018_05_21-PM-00_00_14
Last ObjectModification:
2018_05_19-AM-07_13_33
Theory : core_2
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