Nuprl Lemma : iff_wf
∀[A,B:ℙ]. (A ⇐⇒ B ∈ ℙ)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
member: t ∈ T
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
iff: P ⇐⇒ Q,
prop: ℙ,
and: P ∧ Q,
implies: P ⇒ Q,
rev_implies: P ⇐ Q
Lemmas referenced :
rev_implies_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
introduction,
cut,
sqequalRule,
productEquality,
functionEquality,
sqequalHypSubstitution,
cumulativity,
hypothesisEquality,
extract_by_obid,
isectElimination,
thin,
hypothesis,
axiomEquality,
equalityTransitivity,
equalitySymmetry,
Error :inhabitedIsType,
isect_memberEquality,
universeEquality,
Error :universeIsType
Latex:
\mforall{}[A,B:\mBbbP{}]. (A \mLeftarrow{}{}\mRightarrow{} B \mmember{} \mBbbP{})
Date html generated:
2019_06_20-AM-11_14_32
Last ObjectModification:
2018_09_26-AM-10_41_58
Theory : core_2
Home
Index