Nuprl Lemma : implies_transitivity
∀[P,Q,R:ℙ]. ((P ⇒ Q) ⇒ (Q ⇒ R) ⇒ {P ⇒ R})
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
guard: {T},
implies: P ⇒ Q
Definitions unfolded in proof :
guard: {T},
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ
Rules used in proof :
sqequalSubstitution,
sqequalRule,
sqequalReflexivity,
sqequalTransitivity,
computationStep,
Error :isect_memberFormation_alt,
lambdaFormation,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
hypothesisEquality,
functionEquality,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P,Q,R:\mBbbP{}]. ((P {}\mRightarrow{} Q) {}\mRightarrow{} (Q {}\mRightarrow{} R) {}\mRightarrow{} \{P {}\mRightarrow{} R\})
Date html generated:
2019_06_20-AM-11_16_44
Last ObjectModification:
2018_09_26-AM-10_24_22
Theory : core_2
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