Nuprl Lemma : iff_weakening_uiff
∀[P,Q:ℙ]. (uiff(P;Q) ⇒ (P ⇐⇒ Q))
Proof
Definitions occuring in Statement :
uiff: uiff(P;Q),
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
uiff: uiff(P;Q),
and: P ∧ Q,
iff: P ⇐⇒ Q,
uimplies: b supposing a,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
uiff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
independent_isectElimination,
hypothesis,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. (uiff(P;Q) {}\mRightarrow{} (P \mLeftarrow{}{}\mRightarrow{} Q))
Date html generated:
2019_06_20-AM-11_14_02
Last ObjectModification:
2018_09_26-AM-10_41_47
Theory : core_2
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