Theorem mppsthm

Description: A provable pre-statement is a theorem. (Contributed by Mario Carneiro, 18-Jul-2016)

	Ref	Expression
Hypotheses	mppsthm.j	|- J = ( mPPSt ` T )
	mppsthm.u	|- U = ( mThm ` T )
Assertion	mppsthm	|- J C_ U

Proof

Step	Hyp	Ref	Expression
1		mppsthm.j	|- J = ( mPPSt ` T )
2		mppsthm.u	|- U = ( mThm ` T )
3		eqid	|- ( ( mStRed ` T ) ` x ) = ( ( mStRed ` T ) ` x )
4		eqid	|- ( mStRed ` T ) = ( mStRed ` T )
5	4 1 2	mthmi	|- ( ( x e. J /\ ( ( mStRed ` T ) ` x ) = ( ( mStRed ` T ) ` x ) ) -> x e. U )
6	3 5	mpan2	|- ( x e. J -> x e. U )
7	6	ssriv	|- J C_ U