Nuprl Lemma : curry-lemma
∀A,B,C:ℙ. (((A ∧ B) ⇒ C) ⇒ A ⇒ B ⇒ C)
Proof
Definitions occuring in Statement :
prop: ℙ,
all: ∀x:A. B[x],
implies: P ⇒ Q,
and: P ∧ Q
Definitions unfolded in proof :
prop: ℙ,
member: t ∈ T,
cand: A c∧ B,
and: P ∧ Q,
implies: P ⇒ Q,
all: ∀x:A. B[x]
Rules used in proof :
universeEquality,
cumulativity,
productEquality,
functionEquality,
hypothesisEquality,
independent_pairFormation,
thin,
independent_functionElimination,
sqequalHypSubstitution,
hypothesis,
cut,
lambdaFormation,
sqequalReflexivity,
computationStep,
sqequalTransitivity,
sqequalSubstitution
Latex:
\mforall{}A,B,C:\mBbbP{}. (((A \mwedge{} B) {}\mRightarrow{} C) {}\mRightarrow{} A {}\mRightarrow{} B {}\mRightarrow{} C)
Date html generated:
2016_10_21-AM-09_35_22
Last ObjectModification:
2016_09_23-PM-04_31_02
Theory : core_2
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