Theorem dfvd2an

Description: Definition of a 2-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 23-Apr-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd2an	|- ( (. (. ph ,. ps ). ->. ch ). <-> ( ( ph /\ ps ) -> ch ) )

Proof

Step	Hyp	Ref	Expression
1		df-vd1	|- ( (. (. ph ,. ps ). ->. ch ). <-> ( (. ph ,. ps ). -> ch ) )
2		df-vhc2	|- ( (. ph ,. ps ). <-> ( ph /\ ps ) )
3	2	imbi1i	|- ( ( (. ph ,. ps ). -> ch ) <-> ( ( ph /\ ps ) -> ch ) )
4	1 3	bitri	|- ( (. (. ph ,. ps ). ->. ch ). <-> ( ( ph /\ ps ) -> ch ) )