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Theorem gen21 37040
Description: Virtual deduction generalizing rule for one quantifying variables and two virtual hypothesis. gen21 37040 is alrimdv 1785 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 36997 . . 3  |-  ( ph  ->  ( ps  ->  ch ) )
32alrimdv 1785 . 2  |-  ( ph  ->  ( ps  ->  A. x ch ) )
43dfvd2ir 36998 1  |-  (. ph ,. ps  ->.  A. x ch ).
Colors of variables: wff setvar class
Syntax hints:   A.wal 1452   (.wvd2 36989
This theorem was proved from axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8  ax-gen 1679  ax-4 1692  ax-5 1768
This theorem depends on definitions:  df-bi 190  df-an 377  df-vd2 36990
This theorem is referenced by:  truniALTVD  37314  trintALTVD  37316  onfrALTlem2VD  37325
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