Nuprl Lemma : classical-and
∀[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,
and: 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},
cand: A c∧ B,
prop: ℙ,
unit: Unit
Lemmas referenced :
classical_wf,
and_wf,
it_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
independent_pairFormation,
sqequalHypSubstitution,
productElimination,
thin,
setElimination,
rename,
dependent_set_memberEquality,
lemma_by_obid,
hypothesis,
isectElimination,
hypothesisEquality,
because_Cache,
sqequalRule,
axiomEquality,
natural_numberEquality,
independent_pairEquality,
isect_memberEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality
Latex:
\mforall{}[A,B:\mBbbP{}]. uiff(\{A\} \mwedge{} \{B\};\{A \mwedge{} B\})
Date html generated:
2016_05_13-PM-03_16_47
Last ObjectModification:
2016_01_06-PM-05_20_17
Theory : core_2
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