Nuprl Lemma : iff_transitivity
∀[P,Q,R:ℙ]. ((P ⇐⇒ Q) ⇒ (Q ⇐⇒ R) ⇒ (P ⇐⇒ R))
Proof
Definitions occuring in Statement :
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,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
independent_pairFormation,
independent_functionElimination,
hypothesis,
hypothesisEquality,
cut,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P,Q,R:\mBbbP{}]. ((P \mLeftarrow{}{}\mRightarrow{} Q) {}\mRightarrow{} (Q \mLeftarrow{}{}\mRightarrow{} R) {}\mRightarrow{} (P \mLeftarrow{}{}\mRightarrow{} R))
Date html generated:
2019_06_20-AM-11_16_41
Last ObjectModification:
2018_09_26-AM-10_24_20
Theory : core_2
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