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Theorem iden2 33586
Description: Virtual deduction identity rule. simpr 461 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
StepHypRef Expression
1 simpr 461 . 2  |-  ( (
ph  /\  ps )  ->  ps )
2 dfvd2an 33545 . 2  |-  ( (.
(. ph ,. ps ).  ->.  ps
). 
<->  ( ( ph  /\  ps )  ->  ps )
)
31, 2mpbir 209 1  |-  (. (. ph ,. ps ).  ->.  ps ).
Colors of variables: wff setvar class
Syntax hints:    -> wi 4    /\ wa 369   (.wvd1 33532   (.wvhc2 33543
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-an 371  df-vd1 33533  df-vhc2 33544
This theorem is referenced by: (None)
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