### Nuprl Lemma : and-iff

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

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` iff: `P `⇐⇒` Q` implies: `P `` Q` and: `P ∧ Q` isect: `⋂x:A. B[x]`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` implies: `P `` Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` member: `t ∈ T` prop: `ℙ` rev_implies: `P `` Q` subtype_rel: `A ⊆r 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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