Nuprl Lemma : implies_antisymmetry
∀[P,Q:ℙ]. ((P ⇒ Q) ⇒ (Q ⇒ P) ⇒ (P ⇐⇒ Q))
Proof
Definitions occuring in Statement :
uall: ∀[x:A]. B[x],
prop: ℙ,
iff: P ⇐⇒ Q,
implies: P ⇒ Q
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
implies: P ⇒ Q,
iff: P ⇐⇒ Q,
and: P ∧ Q,
member: t ∈ T,
prop: ℙ,
rev_implies: P ⇐ Q
Rules used in proof :
sqequalSubstitution,
sqequalTransitivity,
computationStep,
sqequalReflexivity,
Error :isect_memberFormation_alt,
lambdaFormation,
independent_pairFormation,
sqequalHypSubstitution,
independent_functionElimination,
thin,
hypothesis,
hypothesisEquality,
functionEquality,
Error :inhabitedIsType,
Error :universeIsType,
universeEquality
Latex:
\mforall{}[P,Q:\mBbbP{}]. ((P {}\mRightarrow{} Q) {}\mRightarrow{} (Q {}\mRightarrow{} P) {}\mRightarrow{} (P \mLeftarrow{}{}\mRightarrow{} Q))
Date html generated:
2019_06_20-AM-11_17_43
Last ObjectModification:
2018_09_26-AM-10_25_05
Theory : core_2
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