### Nuprl Lemma : prime_ideal_p_wf

`∀[r:RngSig]. ∀[P:|r| ⟶ ℙ].  (IsPrimeIdeal(r;P) ∈ ℙ)`

Proof

Definitions occuring in Statement :  prime_ideal_p: `IsPrimeIdeal(R;P)` rng_car: `|r|` rng_sig: `RngSig` uall: `∀[x:A]. B[x]` prop: `ℙ` member: `t ∈ T` function: `x:A ⟶ B[x]`
Definitions unfolded in proof :  prime_ideal_p: `IsPrimeIdeal(R;P)` uall: `∀[x:A]. B[x]` member: `t ∈ T` so_lambda: `λ2x.t[x]` implies: `P `` Q` prop: `ℙ` infix_ap: `x f y` so_apply: `x[s]`
Lemmas referenced :  and_wf not_wf rng_one_wf all_wf rng_car_wf rng_times_wf or_wf rng_sig_wf
Rules used in proof :  sqequalSubstitution sqequalRule sqequalReflexivity sqequalTransitivity computationStep isect_memberFormation introduction cut lemma_by_obid sqequalHypSubstitution isectElimination thin applyEquality hypothesisEquality hypothesis lambdaEquality functionEquality axiomEquality equalityTransitivity equalitySymmetry cumulativity universeEquality isect_memberEquality because_Cache

Latex:
\mforall{}[r:RngSig].  \mforall{}[P:|r|  {}\mrightarrow{}  \mBbbP{}].    (IsPrimeIdeal(r;P)  \mmember{}  \mBbbP{})

Date html generated: 2016_05_15-PM-00_24_43
Last ObjectModification: 2015_12_27-AM-00_00_10

Theory : rings_1

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