Nuprl Lemma : uiff_wf
∀[P,Q:ℙ]. (uiff(P;Q) ∈ ℙ)
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
uiff: uiff(P;Q),
uimplies: b supposing a,
prop: ℙ,
so_lambda: λ2x.t[x],
so_apply: x[s]
Lemmas referenced :
isect_wf,
and_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
cut,
sqequalRule,
lemma_by_obid,
sqequalHypSubstitution,
isectElimination,
thin,
hypothesisEquality,
lambdaEquality,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
universeEquality,
isect_memberEquality,
because_Cache
Latex:
\mforall{}[P,Q:\mBbbP{}]. (uiff(P;Q) \mmember{} \mBbbP{})
Date html generated:
2016_05_13-PM-03_07_16
Last ObjectModification:
2016_01_06-PM-05_28_42
Theory : core_2
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