Theorem cgrrflx2d

Description: Deduction form of axcgrrflx . (Contributed by Scott Fenton, 13-Oct-2013)

	Ref	Expression
Hypotheses	cgrrflx2d.1	|- ( ph -> N e. NN )
	cgrrflx2d.2	|- ( ph -> A e. ( EE ` N ) )
	cgrrflx2d.3	|- ( ph -> B e. ( EE ` N ) )
Assertion	cgrrflx2d	|- ( ph -> <. A , B >. Cgr <. B , A >. )

Proof

Step	Hyp	Ref	Expression
1		cgrrflx2d.1	|- ( ph -> N e. NN )
2		cgrrflx2d.2	|- ( ph -> A e. ( EE ` N ) )
3		cgrrflx2d.3	|- ( ph -> B e. ( EE ` N ) )
4		axcgrrflx	|- ( ( N e. NN /\ A e. ( EE ` N ) /\ B e. ( EE ` N ) ) -> <. A , B >. Cgr <. B , A >. )
5	1 2 3 4	syl3anc	|- ( ph -> <. A , B >. Cgr <. B , A >. )