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Theorem gen21nv 28697
Description: Virtual deduction form of alrimdh 1577. (Contributed by Alan Sare, 31-Dec-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypotheses
Ref Expression
gen21nv.1  |-  ( ph  ->  A. x ph )
gen21nv.2  |-  ( ps 
->  A. x ps )
gen21nv.3  |-  (. ph ,. ps  ->.  ch ).
Assertion
Ref Expression
gen21nv  |-  (. ph ,. ps  ->.  A. x ch ).

Proof of Theorem gen21nv
StepHypRef Expression
1 gen21nv.1 . . 3  |-  ( ph  ->  A. x ph )
2 gen21nv.2 . . 3  |-  ( ps 
->  A. x ps )
3 gen21nv.3 . . . 4  |-  (. ph ,. ps  ->.  ch ).
43dfvd2i 28653 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
51, 2, 4alrimdh 1577 . 2  |-  ( ph  ->  ( ps  ->  A. x ch ) )
65dfvd2ir 28654 1  |-  (. ph ,. ps  ->.  A. x ch ).
Colors of variables: wff set class
Syntax hints:    -> wi 4   A.wal 1530   (.wvd2 28645
This theorem is referenced by:  ssralv2VD  28958
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547
This theorem depends on definitions:  df-bi 177  df-an 360  df-vd2 28646
  Copyright terms: Public domain W3C validator