Nuprl Lemma : and-iff

[A:ℙ]. ∀[B,C:⋂a:A. ℙ].  ((A  (B ⇐⇒ C))  {A ∧ ⇐⇒ A ∧ C})


Proof




Definitions occuring in Statement :  uall: [x:A]. B[x] prop: guard: {T} iff: ⇐⇒ Q implies:  Q and: P ∧ Q isect: x:A. B[x]
Definitions unfolded in proof :  guard: {T} uall: [x:A]. B[x] implies:  Q iff: ⇐⇒ Q and: P ∧ Q member: t ∈ T prop: rev_implies:  Q subtype_rel: A ⊆B
Lemmas referenced :  iff_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation lambdaFormation independent_pairFormation sqequalHypSubstitution productElimination thin hypothesis independent_functionElimination productEquality cumulativity hypothesisEquality cut rename isectElimination equalityTransitivity equalitySymmetry because_Cache functionEquality lemma_by_obid applyEquality lambdaEquality isectEquality universeEquality

Latex:
\mforall{}[A:\mBbbP{}].  \mforall{}[B,C:\mcap{}a:A.  \mBbbP{}].    ((A  {}\mRightarrow{}  (B  \mLeftarrow{}{}\mRightarrow{}  C))  {}\mRightarrow{}  \{A  \mwedge{}  B  \mLeftarrow{}{}\mRightarrow{}  A  \mwedge{}  C\})



Date html generated: 2016_05_13-PM-03_13_08
Last ObjectModification: 2016_01_06-PM-05_23_28

Theory : core_2


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