Nuprl Lemma : iff_symmetry
∀[A,B:ℙ]. (A ⇐⇒ B ⇐⇒ B ⇐⇒ A)
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
iff: P ⇐⇒ Q,
and: P ∧ Q,
implies: P ⇒ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Lemmas referenced :
iff_wf
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
independent_pairFormation,
lambdaFormation,
sqequalHypSubstitution,
productElimination,
thin,
hypothesisEquality,
independent_functionElimination,
hypothesis,
cut,
introduction,
extract_by_obid,
isectElimination,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[A,B:\mBbbP{}]. (A \mLeftarrow{}{}\mRightarrow{} B \mLeftarrow{}{}\mRightarrow{} B \mLeftarrow{}{}\mRightarrow{} A)
Date html generated:
2019_06_20-AM-11_15_52
Last ObjectModification:
2018_09_26-AM-10_23_50
Theory : core_2
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