Nuprl Lemma : classical-implies
∀[A,B:ℙ]. uiff(A ⇒ {B};{A ⇒ B})
Proof
Definitions occuring in Statement :
classical: {P},
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
and: P ∧ Q,
uimplies: b supposing a,
classical: {P},
unit: Unit,
implies: P ⇒ Q,
prop: ℙ,
all: ∀x:A. B[x],
or: P ∨ Q,
not: ¬A,
false: False
Lemmas referenced :
it_wf,
classical-excluded-middle,
classical_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalRule,
sqequalHypSubstitution,
setElimination,
thin,
rename,
dependent_set_memberEquality,
axiomEquality,
natural_numberEquality,
hypothesis,
functionEquality,
hypothesisEquality,
lemma_by_obid,
isectElimination,
lambdaFormation,
lambdaEquality,
dependent_functionElimination,
productElimination,
independent_pairEquality,
isect_memberEquality,
because_Cache,
equalityTransitivity,
equalitySymmetry,
universeEquality,
unionElimination,
independent_functionElimination,
voidElimination
Latex:
\mforall{}[A,B:\mBbbP{}]. uiff(A {}\mRightarrow{} \{B\};\{A {}\mRightarrow{} B\})
Date html generated:
2016_05_13-PM-03_16_42
Last ObjectModification:
2016_01_06-PM-05_21_09
Theory : core_2
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