Nuprl Lemma : set-axiom-of-choice_wf
Set-AC ∈ ℙ'
Proof
Definitions occuring in Statement : 
set-axiom-of-choice: Set-AC
, 
prop: ℙ
, 
member: t ∈ T
Definitions unfolded in proof : 
set-axiom-of-choice: Set-AC
, 
member: t ∈ T
, 
uall: ∀[x:A]. B[x]
, 
so_lambda: λ2x.t[x]
, 
implies: P 
⇒ Q
, 
prop: ℙ
, 
subtype_rel: A ⊆r B
, 
so_apply: x[s]
, 
guard: {T}
, 
uimplies: b supposing a
Lemmas referenced : 
all_wf, 
exists_wf, 
ext-eq_wf, 
equal_wf, 
ext-eq_inversion, 
subtype_rel_weakening
Rules used in proof : 
sqequalSubstitution, 
sqequalRule, 
sqequalReflexivity, 
sqequalTransitivity, 
computationStep, 
cut, 
instantiate, 
introduction, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
thin, 
universeEquality, 
lambdaEquality, 
functionEquality, 
cumulativity, 
hypothesisEquality, 
applyEquality, 
functionExtensionality, 
because_Cache, 
hypothesis, 
independent_isectElimination
Latex:
Set-AC  \mmember{}  \mBbbP{}'
Date html generated:
2017_04_14-AM-07_37_38
Last ObjectModification:
2017_02_27-PM-03_09_52
Theory : subtype_1
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