Nuprl Lemma : fo-logic-xmiddle
∀x:Dom. ((((B x) ∨ ((B x) 
⇒ A)) 
⇒ A) 
⇒ A)
Proof
Definitions occuring in Statement : 
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H])
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
or: P ∨ Q
, 
apply: f a
Definitions unfolded in proof : 
language1: language1{i:l}(D,A,B,C,P,Q,R,H.fml[D;A;B;C;P;Q;R;H])
, 
uall: ∀[x:A]. B[x]
, 
!hyp_hide: x
, 
member: t ∈ T
, 
prop: ℙ
, 
all: ∀x:A. B[x]
, 
implies: P 
⇒ Q
, 
guard: {T}
, 
or: P ∨ Q
Lemmas referenced : 
or_wf
Rules used in proof : 
sqequalSubstitution, 
sqequalTransitivity, 
computationStep, 
sqequalReflexivity, 
isect_memberFormation, 
sqequalHypSubstitution, 
functionEquality, 
cumulativity, 
hypothesisEquality, 
universeEquality, 
because_Cache, 
lambdaFormation, 
cut, 
lemma_by_obid, 
isectElimination, 
thin, 
applyEquality, 
hypothesis, 
addLevel, 
independent_functionElimination, 
levelHypothesis, 
sqequalRule, 
inrFormation, 
inlFormation
Latex:
\mforall{}x:Dom.  ((((B  x)  \mvee{}  ((B  x)  {}\mRightarrow{}  A))  {}\mRightarrow{}  A)  {}\mRightarrow{}  A)
Date html generated:
2016_05_16-AM-09_08_03
Last ObjectModification:
2015_12_28-PM-07_03_16
Theory : first-order!and!ancestral!logic
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