Nuprl Lemma : symmetry-preserves-congruence
∀e:BasicGeometry. ∀A,P,Q,p,q:Point.  (p=A=P ⇒ q=A=Q ⇒ PQ ≅ pq)
Proof
Definitions occuring in Statement : 
basic-geometry: BasicGeometry, 
geo-midpoint: a=m=b, 
geo-congruent: ab ≅ cd, 
geo-point: Point, 
all: ∀x:A. B[x], 
implies: P ⇒ Q
Lemmas referenced : 
geo-midpoint-diagonals-congruent
Rules used in proof : 
cut, 
introduction, 
extract_by_obid, 
hypothesis
Latex:
\mforall{}e:BasicGeometry.  \mforall{}A,P,Q,p,q:Point.    (p=A=P  {}\mRightarrow{}  q=A=Q  {}\mRightarrow{}  PQ  \mcong{}  pq)
Date html generated:
2019_10_16-PM-01_28_19
Last ObjectModification:
2019_08_26-PM-09_12_10
Theory : euclidean!plane!geometry
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