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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