Theorem srabaseOLD

Description: Obsolete proof of srabase as of 29-Oct-2024. Base set of a subring algebra. (Contributed by Stefan O'Rear, 27-Nov-2014) (Revised by Mario Carneiro, 4-Oct-2015) (Revised by Thierry Arnoux, 16-Jun-2019) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Hypotheses	srapart.a	|- ( ph -> A = ( ( subringAlg ` W ) ` S ) )
	srapart.s	|- ( ph -> S C_ ( Base ` W ) )
Assertion	srabaseOLD	|- ( ph -> ( Base ` W ) = ( Base ` A ) )

Proof

Step	Hyp	Ref	Expression
1		srapart.a	|- ( ph -> A = ( ( subringAlg ` W ) ` S ) )
2		srapart.s	|- ( ph -> S C_ ( Base ` W ) )
3		df-base	|- Base = Slot 1
4		1nn	|- 1 e. NN
5		1lt5	|- 1 < 5
6	5	orci	|- ( 1 < 5 \/ 8 < 1 )
7	1 2 3 4 6	sralemOLD	|- ( ph -> ( Base ` W ) = ( Base ` A ) )