Nuprl Lemma : mFOLisImp_wf
∀[A:mFOL()]. (mFOLisImp(A) ∈ 𝔹)
Proof
Definitions occuring in Statement : 
mFOLisImp: mFOLisImp(A)
, 
mFOL: mFOL()
, 
bool: 𝔹
, 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
mFOLisImp: mFOLisImp(A)
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
bool: 𝔹
, 
unit: Unit
, 
it: ⋅
, 
btrue: tt
, 
band: p ∧b q
, 
ifthenelse: if b then t else f fi 
, 
uiff: uiff(P;Q)
, 
and: P ∧ Q
, 
uimplies: b supposing a
, 
bfalse: ff
, 
prop: ℙ
Lemmas referenced : 
mFOconnect?_wf, 
bool_wf, 
eqtt_to_assert, 
eq_atom_wf, 
mFOconnect-knd_wf, 
equal_wf, 
mFOL_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
introduction, 
cut, 
sqequalRule, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
hypothesisEquality, 
hypothesis, 
lambdaFormation, 
unionElimination, 
equalityElimination, 
productElimination, 
independent_isectElimination, 
because_Cache, 
tokenEquality, 
equalityTransitivity, 
equalitySymmetry, 
dependent_functionElimination, 
independent_functionElimination, 
axiomEquality
Latex:
\mforall{}[A:mFOL()].  (mFOLisImp(A)  \mmember{}  \mBbbB{})
Date html generated:
2018_05_21-PM-10_24_56
Last ObjectModification:
2017_07_26-PM-06_38_43
Theory : minimal-first-order-logic
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