Theorem caovordd

Description: Convert an operation ordering law to class notation. (Contributed by Mario Carneiro, 30-Dec-2014)

	Ref	Expression
Hypotheses	caovordg.1	|- ( ( ph /\ ( x e. S /\ y e. S /\ z e. S ) ) -> ( x R y <-> ( z F x ) R ( z F y ) ) )
	caovordd.2	|- ( ph -> A e. S )
	caovordd.3	|- ( ph -> B e. S )
	caovordd.4	|- ( ph -> C e. S )
Assertion	caovordd	|- ( ph -> ( A R B <-> ( C F A ) R ( C F B ) ) )

Proof

Step	Hyp	Ref	Expression
1		caovordg.1	|- ( ( ph /\ ( x e. S /\ y e. S /\ z e. S ) ) -> ( x R y <-> ( z F x ) R ( z F y ) ) )
2		caovordd.2	|- ( ph -> A e. S )
3		caovordd.3	|- ( ph -> B e. S )
4		caovordd.4	|- ( ph -> C e. S )
5		id	|- ( ph -> ph )
6	1	caovordg	|- ( ( ph /\ ( A e. S /\ B e. S /\ C e. S ) ) -> ( A R B <-> ( C F A ) R ( C F B ) ) )
7	5 2 3 4 6	syl13anc	|- ( ph -> ( A R B <-> ( C F A ) R ( C F B ) ) )