Nuprl Lemma : prop_and_wf
∀[T:Type]. ∀[P,Q:T ⟶ ℙ].  (P ∧ Q ∈ T ⟶ ℙ)
Proof
Definitions occuring in Statement : 
prop_and: P ∧ Q
, 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
member: t ∈ T
, 
function: x:A ⟶ B[x]
, 
universe: Type
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
member: t ∈ T
, 
prop_and: P ∧ Q
, 
prop: ℙ
, 
and: P ∧ Q
, 
subtype_rel: A ⊆r B
Lemmas referenced : 
subtype_rel_self
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
introduction, 
cut, 
sqequalRule, 
lambdaEquality, 
productEquality, 
applyEquality, 
hypothesisEquality, 
hypothesis, 
thin, 
instantiate, 
extract_by_obid, 
sqequalHypSubstitution, 
isectElimination, 
universeEquality, 
because_Cache, 
axiomEquality, 
equalityTransitivity, 
equalitySymmetry, 
Error :inhabitedIsType, 
isect_memberEquality, 
functionEquality, 
cumulativity, 
Error :functionIsType, 
Error :universeIsType
Latex:
\mforall{}[T:Type].  \mforall{}[P,Q:T  {}\mrightarrow{}  \mBbbP{}].    (P  \mwedge{}  Q  \mmember{}  T  {}\mrightarrow{}  \mBbbP{})
Date html generated:
2019_06_20-PM-00_31_39
Last ObjectModification:
2018_09_26-AM-11_46_31
Theory : relations
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