### Nuprl Lemma : uiff_functionality_wrt_uiff2

`∀[P1,P2,Q1,Q2:ℙ].  ({P1 `⇐⇒` P2} `` {Q1 `⇐⇒` Q2} `` {uiff(P1;Q1) `⇐⇒` uiff(P2;Q2)})`

Proof

Definitions occuring in Statement :  uiff: `uiff(P;Q)` uall: `∀[x:A]. B[x]` prop: `ℙ` guard: `{T}` iff: `P `⇐⇒` Q` implies: `P `` Q`
Definitions unfolded in proof :  guard: `{T}` uall: `∀[x:A]. B[x]` implies: `P `` Q` iff: `P `⇐⇒` Q` and: `P ∧ Q` uiff: `uiff(P;Q)` uimplies: `b supposing a` prop: `ℙ` member: `t ∈ T` rev_implies: `P `` Q`
Lemmas referenced :  uiff_wf and_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep Error :isect_memberFormation_alt,  lambdaFormation sqequalHypSubstitution productElimination thin independent_pairFormation cut hypothesis independent_functionElimination independent_isectElimination Error :universeIsType,  hypothesisEquality introduction extract_by_obid isectElimination functionEquality cumulativity Error :inhabitedIsType,  universeEquality

Latex:
\mforall{}[P1,P2,Q1,Q2:\mBbbP{}].    (\{P1  \mLeftarrow{}{}\mRightarrow{}  P2\}  {}\mRightarrow{}  \{Q1  \mLeftarrow{}{}\mRightarrow{}  Q2\}  {}\mRightarrow{}  \{uiff(P1;Q1)  \mLeftarrow{}{}\mRightarrow{}  uiff(P2;Q2)\})

Date html generated: 2019_06_20-AM-11_14_08
Last ObjectModification: 2018_09_26-AM-10_41_46

Theory : core_2

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