Theorem iden2 38839

Description: Virtual deduction identity rule. simpr 477 in conjunction form Virtual Deduction notation. (Contributed by Alan Sare, 5-Sep-2016.) (Proof modification is discouraged.) (New usage is discouraged.)

Assertion

Ref	Expression
iden2	|- (. (. ph ,. ps ). ->. ps ).

Proof of Theorem iden2

Step	Hyp	Ref	Expression
1		simpr 477	. 2 |- ( ( ph /\ ps ) -> ps )
2		dfvd2an 38798	. 2 |- ( (. (. ph ,. ps ). ->. ps ). <-> ( ( ph /\ ps ) -> ps ) )
3	1, 2	mpbir 221	1 |- (. (. ph ,. ps ). ->. ps ).

Syntax hints:   -> wi 4   /\ 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-an 386  df-vd1 38786  df-vhc2 38797

This theorem is referenced by: (None)