Theorem dfvd3an

Description: Definition of a 3-hypothesis virtual deduction in vd conjunction form. (Contributed by Alan Sare, 13-Jun-2015) (Proof modification is discouraged.) (New usage is discouraged.)

	Ref	Expression
Assertion	dfvd3an	|- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )

Proof

Step	Hyp	Ref	Expression
1		df-vd1	|- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( (. ph ,. ps ,. ch ). -> th ) )
2		df-vhc3	|- ( (. ph ,. ps ,. ch ). <-> ( ph /\ ps /\ ch ) )
3	2	imbi1i	|- ( ( (. ph ,. ps ,. ch ). -> th ) <-> ( ( ph /\ ps /\ ch ) -> th ) )
4	1 3	bitri	|- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )