Theorem gausslemma2dlem0a

Description: Auxiliary lemma 1 for gausslemma2d . (Contributed by AV, 9-Jul-2021)

	Ref	Expression
Hypothesis	gausslemma2dlem0a.p	|- ( ph -> P e. ( Prime \ { 2 } ) )
Assertion	gausslemma2dlem0a	|- ( ph -> P e. NN )

Proof

Step	Hyp	Ref	Expression
1		gausslemma2dlem0a.p	|- ( ph -> P e. ( Prime \ { 2 } ) )
2		nnoddn2prm	|- ( P e. ( Prime \ { 2 } ) -> ( P e. NN /\ -. 2 || P ) )
3		simpl	|- ( ( P e. NN /\ -. 2 || P ) -> P e. NN )
4	1 2 3	3syl	|- ( ph -> P e. NN )