Nuprl Lemma : and_false_r
∀[A:ℙ]. (A ∧ False 
⇐⇒ False)
Proof
Definitions occuring in Statement : 
uall: ∀[x:A]. B[x]
, 
prop: ℙ
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
false: False
Definitions unfolded in proof : 
uall: ∀[x:A]. B[x]
, 
iff: P 
⇐⇒ Q
, 
and: P ∧ Q
, 
implies: P 
⇒ Q
, 
false: False
, 
member: t ∈ T
, 
prop: ℙ
, 
rev_implies: P 
⇐ Q
Lemmas referenced : 
false_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
Error :isect_memberFormation_alt, 
independent_pairFormation, 
lambdaFormation, 
cut, 
sqequalHypSubstitution, 
productElimination, 
thin, 
voidElimination, 
hypothesis, 
productEquality, 
cumulativity, 
hypothesisEquality, 
introduction, 
extract_by_obid, 
Error :universeIsType, 
universeEquality
Latex:
\mforall{}[A:\mBbbP{}].  (A  \mwedge{}  False  \mLeftarrow{}{}\mRightarrow{}  False)
Date html generated:
2019_06_20-AM-11_16_11
Last ObjectModification:
2018_09_26-AM-10_24_03
Theory : core_2
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