Theorem dfvd2 38795

Description: Definition of a 2-hypothesis virtual deduction. (Contributed by Alan Sare, 14-Nov-2011.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
dfvd2	|- ( (. ph ,. ps ->. ch ). <-> ( ph -> ( ps -> ch ) ) )

Proof of Theorem dfvd2

Step	Hyp	Ref	Expression
1		df-vd2 38794	. 2 |- ( (. ph ,. ps ->. ch ). <-> ( ( ph /\ ps ) -> ch ) )
2		impexp 462	. 2 |- ( ( ( ph /\ ps ) -> ch ) <-> ( ph -> ( ps -> ch ) ) )
3	1, 2	bitri 264	1 |- ( (. ph ,. ps ->. ch ). <-> ( ph -> ( ps -> ch ) ) )

Syntax hints:   -> wi 4   <-> wb 196   /\ wa 384   (.wvd2 38793

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-an 386  df-vd2 38794

This theorem is referenced by:  dfvd2i  38801  dfvd2ir  38802  dfvd2imp  38828  dfvd2impr  38829