Theorem dfvd3an 31194

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.)

Assertion

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

Proof of Theorem dfvd3an

Step	Hyp	Ref	Expression
1		df-vd1 31170	. 2 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( (. ph ,. ps ,. ch ). -> th ) )
2		df-vhc3 31189	. . 3 |- ( (. ph ,. ps ,. ch ). <-> ( ph /\ ps /\ ch ) )
3	2	imbi1i 325	. 2 |- ( ( (. ph ,. ps ,. ch ). -> th ) <-> ( ( ph /\ ps /\ ch ) -> th ) )
4	1, 3	bitri 249	1 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )

Syntax hints:   -> wi 4   <-> wb 184   /\ w3a 965   (.wvd1 31169   (.wvhc3 31188

This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem depends on definitions:  df-bi 185  df-vd1 31170  df-vhc3 31189

This theorem is referenced by:  dfvd3ani  31195  dfvd3anir  31196