Nuprl Lemma : xmiddle-elim2
∀[P:ℙ]. (((P ∨ (¬P)) ⇒ False) ⇒ False)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
false: False
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
member: t ∈ T,
not: ¬A,
implies: P ⇒ Q,
or: P ∨ Q,
prop: ℙ
Lemmas referenced :
false_wf,
or_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
isect_memberFormation,
introduction,
lambdaEquality,
applyEquality,
hypothesisEquality,
inrEquality,
inlEquality,
functionEquality,
sqequalHypSubstitution,
cumulativity,
cut,
extract_by_obid,
hypothesis,
isectElimination,
thin,
universeEquality
Latex:
\mforall{}[P:\mBbbP{}]. (((P \mvee{} (\mneg{}P)) {}\mRightarrow{} False) {}\mRightarrow{} False)
Date html generated:
2019_10_15-AM-11_32_58
Last ObjectModification:
2018_08_25-PM-02_14_06
Theory : general
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