Theorem dfvd2an 38798

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.)

Assertion

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

Proof of Theorem dfvd2an

Step	Hyp	Ref	Expression
1		df-vd1 38786	. 2 |- ( (. (. ph ,. ps ). ->. ch ). <-> ( (. ph ,. ps ). -> ch ) )
2		df-vhc2 38797	. . 3 |- ( (. ph ,. ps ). <-> ( ph /\ ps ) )
3	2	imbi1i 339	. 2 |- ( ( (. ph ,. ps ). -> ch ) <-> ( ( ph /\ ps ) -> ch ) )
4	1, 3	bitri 264	1 |- ( (. (. ph ,. ps ). ->. ch ). <-> ( ( ph /\ ps ) -> ch ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   (.wvd1 38785   (.wvhc2 38796

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 197  df-vd1 38786  df-vhc2 38797

This theorem is referenced by:  dfvd2ani  38799  dfvd2anir  38800  iden2  38839