Theorem dfvd3an 28395

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 28370	. 2 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( (. ph ,. ps ,. ch ). -> th ) )
2		df-vhc3 28390	. . 3 |- ( (. ph ,. ps ,. ch ). <-> ( ph /\ ps /\ ch ) )
3	2	imbi1i 316	. 2 |- ( ( (. ph ,. ps ,. ch ). -> th ) <-> ( ( ph /\ ps /\ ch ) -> th ) )
4	1, 3	bitri 241	1 |- ( (. (. ph ,. ps ,. ch ). ->. th ). <-> ( ( ph /\ ps /\ ch ) -> th ) )

Syntax hints:   -> wi 4   <-> wb 177   /\ w3a 936   (.wvd1 28369   (.wvhc3 28389

This theorem is referenced by:  dfvd3ani  28396  dfvd3anir  28397

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

This theorem depends on definitions:  df-bi 178  df-vd1 28370  df-vhc3 28390