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Theorem gen21 28696
Description: Virtual deduction generalizing rule for 1 quantifying variables and 2 virtual hypothesis. gen21 28696 is alrimdv 1623 with virtual deductions. (Contributed by Alan Sare, 25-Jul-2011.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen21.1  |-  (. ph ,. ps  ->.  ch ).
Assertion
Ref Expression
gen21  |-  (. ph ,. ps  ->.  A. x ch ).
Distinct variable groups:    ph, x    ps, x
Allowed substitution hint:    ch( x)

Proof of Theorem gen21
StepHypRef Expression
1 gen21.1 . . . 4  |-  (. ph ,. ps  ->.  ch ).
21dfvd2i 28653 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32alrimdv 1623 . 2  |-  ( ph  ->  ( ps  ->  A. x ch ) )
43dfvd2ir 28654 1  |-  (. ph ,. ps  ->.  A. x ch ).
Colors of variables: wff set class
Syntax hints:   A.wal 1530   (.wvd2 28645
This theorem is referenced by:  truniALTVD  28970  trintALTVD  28972  onfrALTlem2VD  28981
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1536  ax-5 1547  ax-17 1606
This theorem depends on definitions:  df-bi 177  df-an 360  df-vd2 28646
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