Theorem zlmbas

Description: Base set of a ZZ -module. (Contributed by Mario Carneiro, 2-Oct-2015)

	Ref	Expression
Hypotheses	zlmbas.w	|- W = ( ZMod ` G )
	zlmbas.2	|- B = ( Base ` G )
Assertion	zlmbas	|- B = ( Base ` W )

Proof

Step	Hyp	Ref	Expression
1		zlmbas.w	|- W = ( ZMod ` G )
2		zlmbas.2	|- B = ( Base ` G )
3		df-base	|- Base = Slot 1
4		1nn	|- 1 e. NN
5		1lt5	|- 1 < 5
6	1 3 4 5	zlmlem	|- ( Base ` G ) = ( Base ` W )
7	2 6	eqtri	|- B = ( Base ` W )