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Theorem gen31 27766
Description: Virtual deduction generalizing rule for 1 quantifying variable and 3 virtual hypothesis. gen31 27766 is ggen31 27683 with virtual deductions. (Contributed by Alan Sare, 22-Jun-2012.) (Proof modification is discouraged.) (New usage is discouraged.)
Hypothesis
Ref Expression
gen31.1  |-  (. ph ,. ps ,. ch  ->.  th ).
Assertion
Ref Expression
gen31  |-  (. ph ,. ps ,. ch  ->.  A. x th ).
Distinct variable groups:    ch, x    ph, x    ps, x
Allowed substitution hint:    th( x)

Proof of Theorem gen31
StepHypRef Expression
1 gen31.1 . . . 4  |-  (. ph ,. ps ,. ch  ->.  th ).
21dfvd3i 27734 . . 3  |-  ( ph  ->  ( ps  ->  ( ch  ->  th ) ) )
32ggen31 27683 . 2  |-  ( ph  ->  ( ps  ->  ( ch  ->  A. x th )
) )
43dfvd3ir 27735 1  |-  (. ph ,. ps ,. ch  ->.  A. x th ).
Colors of variables: wff set class
Syntax hints:   A.wal 1527   (.wvd3 27729
This theorem is referenced by:  onfrALTlem2VD  28038
This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-3 7  ax-mp 8  ax-gen 1533  ax-5 1544  ax-17 1603
This theorem depends on definitions:  df-bi 177  df-an 360  df-3an 936  df-vd3 27732
  Copyright terms: Public domain W3C validator