Theorem stm1ri

Description: State of component of unit meet. (Contributed by NM, 11-Nov-1999) (New usage is discouraged.)

	Ref	Expression
Hypotheses	stle.1	|- A e. CH
	stle.2	|- B e. CH
Assertion	stm1ri	|- ( S e. States -> ( ( S ` ( A i^i B ) ) = 1 -> ( S ` B ) = 1 ) )

Proof

Step	Hyp	Ref	Expression
1		stle.1	|- A e. CH
2		stle.2	|- B e. CH
3		incom	|- ( A i^i B ) = ( B i^i A )
4	3	fveq2i	|- ( S ` ( A i^i B ) ) = ( S ` ( B i^i A ) )
5	4	eqeq1i	|- ( ( S ` ( A i^i B ) ) = 1 <-> ( S ` ( B i^i A ) ) = 1 )
6	2 1	stm1i	|- ( S e. States -> ( ( S ` ( B i^i A ) ) = 1 -> ( S ` B ) = 1 ) )
7	5 6	biimtrid	|- ( S e. States -> ( ( S ` ( A i^i B ) ) = 1 -> ( S ` B ) = 1 ) )