### Nuprl Lemma : and_functionality_wrt_iff

`∀[P1,P2,Q1,Q2:ℙ].  ((P1 `⇐⇒` P2) `` (Q1 `⇐⇒` Q2) `` (P1 ∧ Q1 `⇐⇒` P2 ∧ Q2))`

Proof

Definitions occuring in Statement :  uall: `∀[x:A]. B[x]` prop: `ℙ` iff: `P `⇐⇒` Q` implies: `P `` Q` and: `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`
Lemmas referenced :  iff_wf
Rules used in proof :  sqequalSubstitution sqequalTransitivity computationStep sqequalReflexivity Error :isect_memberFormation_alt,  lambdaFormation sqequalHypSubstitution productElimination thin independent_pairFormation independent_functionElimination hypothesis productEquality cumulativity hypothesisEquality cut introduction extract_by_obid isectElimination Error :inhabitedIsType,  Error :universeIsType,  universeEquality

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

Date html generated: 2019_06_20-AM-11_16_46
Last ObjectModification: 2018_09_26-AM-10_24_23

Theory : core_2

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